Am 10.12.2019 ist der langersehnte Referentenentwurf eines Gesetzes zur Umsetzung der Anti-Steuer... more Am 10.12.2019 ist der langersehnte Referentenentwurf eines Gesetzes zur Umsetzung der Anti-Steuervermeidungsrichtlinie (ATAD-Umsetzungsgesetz – ATADUmsG) veröffentlicht worden, diesmal sogar „offiziell“. Der Beitrag versteht sich insoweit als „Update“ zu dem bereits von Haase/Hofacker besprochenen „inoffiziellen“ Gesetzesentwurf vom Dezember 2018 (Ubg 2019, 260). Vorliegend werden zur Vermeidung von Wiederholungen nur die Änderungen gegenüber dieser „Kleinen Lösung“ herausgearbeitet, die sich zwar vom Umfang her im Rahmen halten, aber dem Rechtsanwender dennoch Überraschendes bieten. Der Beitrag wird abgerundet durch Kurzhinweise zu nun erstmals bekanntgewordenen Neuerungen im Anwendungsbereich der §§ 1 und 6 AStG sowie zur Neueinführung eines § 4k EStG. Der ursprünglich sehr kurzfristig für den 18.12.2019 geplante Kabinettsbeschluss wurde gleichsam „in letzter Sekunde“ wieder abgesagt und in das neue Jahr vertagt. Hoffentlich nimmt der Gesetzgeber die gewonnene Zeit zum Anlass, das Gesetz noch einmal inhaltlich zu überdenken.
Rainfall is natural climatic phenomena whose prediction is challenging and demanding. Worldwide n... more Rainfall is natural climatic phenomena whose prediction is challenging and demanding. Worldwide numerous attempts have been made to predict its behavioral pattern using various techniques. The present study is to find a suitable seasonal forecasting model for forecasting monthly rainfall in Tamilnadu. For this purpose, a dataset containing a total of 136 years (1871-2006) monthly rainfall totals of Tamilnadu is obtained from Indian Institute of Tropical Meteorology (IITM), Pune, India and the suitable forecasting model is identified through Box-Jenkins SARIMA modeling.
This research is about an intervention on daily exchange rates of the Nigerian Naira (NGN) and it... more This research is about an intervention on daily exchange rates of the Nigerian Naira (NGN) and its Ugandan counterpart, the Shilling (UGX) observed on 22 nd June 2016. The realization of this time series studied spans from 19 th May 2016 to 17 th November 2016. There is an abrupt jump in the amount of Naira exchanged for a shilling from 0.0509 to 0.0609 from 20 th June to 21 st June 2016 and then to 0.0840 the next day. Instead of coming down it has been moving up. The proposal of an intervention or interrupted time series model to explain this trend of events is the aim of this work. The pre-intervention exchange rates show an initial downward trend up to 26 th May 2016 and then an upward trend. They are adjudged to be non-stationary by the Augmented Dickey Fuller (ADF) test, necessitating their first order differencing. These differences are now stationary and are observed to have a random error fit. Post-intervention forecasts are made on the basis of this pre-intervention model....
A look at the time plot of daily amounts of British pound (GBP) per Euro (EUR) from 17 th as the ... more A look at the time plot of daily amounts of British pound (GBP) per Euro (EUR) from 17 th as the point of intervention. It is noteworthy that on the previous day 23 rd June 2016, the nation of Great Britain voted to opt out of European Union in what is known as Brexit. It is speculated here that this observed relative depreciation of the GBP is caused by this Brexit event. This work is aimed at studying this intervention situation. The pre-intervention exchange rates are adjudged to be non-stationary. Non-seasonal differencing makes it stationary and these differences have the autocorrelation structure of a white noise process. Post-intervention forecasts on the basis of this model are obtained and differences between these and the actual post-intervention observations are modeled for the intervention transfer function. The overall intervention model is observed to be significant and to agree closely with the actual observations. Out-of-sample forecasts comparison shows that forecas...
Journal of the Nigerian Association of Mathematical Physics, 2009
The efficiencies of eight autoregressive model order determination criteria: AIC, BIC, SIC, S, F,... more The efficiencies of eight autoregressive model order determination criteria: AIC, BIC, SIC, S, F, FPE4, CAT2, CAT3, for the selection of subset models are compared using artificial and real series. Our observation is that BIC, S and FPE4 performed well in a wide range of models.
Many economic and business time series exhibit seasonal tendencies. Analytical techniques for suc... more Many economic and business time series exhibit seasonal tendencies. Analytical techniques for such series which take into account these tendencies have engaged the attention of researchers of recent. One such modelling technique is the BoxJenkins seasonal autoregressive integrated moving average (SARIMA) technique. A novel algorithm is hereby proposed. This algorithm which is based on autoregressive-moving average duality arguments is applied to model daily exchange rates of the British pound sterling and the European Euro currencies. The data analyzed are 178 daily pound/euro exchange rates 13 th December 2015 to 7 th June 2016. Application of the algorithm using the SARIMA(1,1,1)x(1,1,1)7 template as proposed yields a SARIMA(1,1,1)x(0,1,1)7 model. Further 8 values from 8 th June to 15 th June 2016 are used for out-of-sample comparison of observations with forecasts. The adequacy of the chosen model is not in doubt since the residuals are uncorrelated and are normally distributed. ...
This is a study of the relative performance of nine automatic autoregressive order determination ... more This is a study of the relative performance of nine automatic autoregressive order determination criteria for full-order modeling using the least squares approach. Of the nine: AIC, FPE, CAT 2 , S, FPE4, Φ, SIC, BIC and CAT 3 , we have found the trio, AIC, FPE and CAT 3 , to be the most consistent. The rest underestimate relatively. Journal of the Nigerian Association of Mathematical Physics , Volume 15 (November, 2009), pp 117 – 122
A realisation, TBR, of Nigeria Treasury Bill Rates from January 2006 to December 2014 is analysed... more A realisation, TBR, of Nigeria Treasury Bill Rates from January 2006 to December 2014 is analysed by seasonal ARIMA methods. The time plot of the realisation reveals an overall downward trend from 2006 to 2009 followed by an overall upward trend up to 2013. Twelve-monthly differencing of TBR yields the series SDTBR which has an overall upward trend. Nonseasonal differencing of SDTBR yields the series DSDTBR with an overall horizontal trend and no clear seasonality. By the Augmented Dickey-Fuller Unit Root Test both TBR and SDTBR are adjudged non-stationary whereas DSDTBR is adjudged stationary. The correlogram of DSDTBR has a negative significant spike in the autocorrelation function at lag 12, an indication of seasonality of period 12 months and the presence of a seasonal moving average component of order one. By a novel proposal credited to Suhartono, initially the (0, 1, 1)x(0, 1, 1)12 SARIMA model is fitted. The non-significance of the lag 13 coefficient suggests the additive SA...
This work is a time series analysis of the monthly domestic consumption of Nigerian Petroleum pro... more This work is a time series analysis of the monthly domestic consumption of Nigerian Petroleum products. The realization analyzed is a 110-point series which spans from July 2006 to August 2015. A time plot of the data shows a generally downward trend. Even though the Augmented Dickey Fuller Unit Root Test is significant, the series could not be said to be stationary because its correlogram reveals an underlying trend and a 12 monthly seasonality. A seasonal difference of the series shows no trend. Its correlogram is suggestive of a seasonal autoregressive integrated moving average (SARIMA) model of order (0,0,1)x(1,1,1) . Diagnostic checking 12 confirms its adequacy. For instance its residuals are largely uncorrelated and are normally distributed. Forecasting and simulations of the monthly domestic consumption quantities could therefore be done using the model.
A brief history of the exchange rates between the Uganda shilling and the United States dollars i... more A brief history of the exchange rates between the Uganda shilling and the United States dollars is given. Moreover, this work involves modeling of their monthly exchange rates by seasonal Box-Jenkins methods. Clearly with time more shillings are exchanged for the dollar, an evidence of relative depreciation of the shilling. An inspection of a realization of the time series which covers from July 1990 to November 2014 reveals a 12-monthly seasonality. A 12-monthly seasonal differencing and then a non-seasonal differencing of the seasonal differences is enough to rid the series of non-stationarity. The autocorrelation structure of the resultant series suggests two seasonal autoregressive integrated moving average (SARIMA) models of orders: (0, 1, 1)x(0, 1, 1)12 and (0, 1, 1)x(1, 1, 1)12. Diagnostic checking shows that the former is the more adequate on all counts. It is therefore recommended that forecasting of the series be based on it.
The time plot of the series NEER shows an overall positive trend with a peak in early 2010 after ... more The time plot of the series NEER shows an overall positive trend with a peak in early 2010 after a deep depression in late 2008. No seasonality is discernible by this visual inspection. Seasonal (i.e. 12-month) differencing yields SDNEER which exhibits an overall slightly positive trend and a high peak in late 2009. Still the visual inspection of the time plot in Figure 2 hardly makes any seasonality obvious. A non-seasonal differencing of SDNEER yields DSDNEER with an overall horizontal trend. Though the time plot in Figure 3 does not give an impression of any regular seasonality, the correlogram of Figure 4 reveals seasonality of period 12 months. Besides there is indication that the product of two moving average components both of order one is involved: one component is seasonal and the other non-seasonal. In addition to that a significant spike of the partial autocorrelation function at lag 12 suggests the involvement of a seasonal autoregressive component of order one. Therefo...
The capital budgeting problem is a multi-constraint Knapsack problem. Hence this paper provides a... more The capital budgeting problem is a multi-constraint Knapsack problem. Hence this paper provides a solution to a capital budgeting problem of Akwa Ibom State, Nigeria using a Branch and Bound approach. The capital projects are summarized in four broad groups: The Economic sector ( ) x , The Social Service sector ( ) x , The Environmental/Regional Development sector ( ) x , and The Administration sector ( ) x . Using Tora software (version 11) for the analysis, it was observed that the optimal solution was found in node 60 while the upper bound and the lower bound were 154.46 and 129.76 respectively. The result shows that the second and the third sector will be selected
A 149-point realization of daily exchange rates of the Uganda shilling (UGX)-Nigerian naira (NGN)... more A 149-point realization of daily exchange rates of the Uganda shilling (UGX)-Nigerian naira (NGN) from 4 th October, 2014 to 1 st March, 2015, is analyzed by Box-Jenkins methods. By a new fitting algorithm, it is concluded that the time series follows the subset SARIMA (1,1,0)x(1,1,0) 7 model. Daily exchange rates between the two currencies may be simulated or forecasted by the model. Introduction Foreign exchange is a major issue in the discussion of world economy. Any trade relationship between the country Uganda and the country Nigeria is based on the relative value of the Uganda Shilling (UGX) and the Nigerian Naira (NGN). In this write-up the daily exchange rates shall be modelled by Box-Jenkins methods. The particular approach shall be the seasonal autoregressive integrated moving average (SARIMA) approach proposed by Box et al. [1]. In recent times, many authors have adopted the SARIMA modelling approach to model real life data. Jianfeng (2013) noticed that SARIMA modelling r...
We consider a dynamic stochastic knapsack problem with the aim of minimizing the cost of the sele... more We consider a dynamic stochastic knapsack problem with the aim of minimizing the cost of the selected items whose weights follow a mixture of Poisson and Exponential distribution using additive model. A graphical presentation of our contagious distribution with different values of both parameters and range of X is made to show their behaviors. We also propose an algebraic model for the problem.
Background: The Central Bank of Nigeria has itemized Nigerian real Gross Domestic Product (GDP) i... more Background: The Central Bank of Nigeria has itemized Nigerian real Gross Domestic Product (GDP) into the following: crop production, livestock, forestry, fishing, crude petroleum and natural gas, solid minerals, manufacturing, construction, trade, transport, information and communication, utilities, accommodation and food services, finance and insurance, real estate, professional, scientific and technical services, administrative, support and business services, public administration, education, human health and social services, arts, entertainment and recreation and other services. Objective: This paper is an attempt to break Nigerian real GDP into clusters on the basis of their contributions in the year 2018 and the first three quarters of 2019. Methodology: The researcher made use of a combination of two distances: (i) the Pearson’s (correlation coefficient) distance and (ii) the absolute correlation coefficient distance to assist into breaking Nigeria’s GDP into clusters. Addi...
A realization of monthly Nigerian crude oil domestic production, NODP, from January 2006 to Augus... more A realization of monthly Nigerian crude oil domestic production, NODP, from January 2006 to August 2012, is analyzed. The time plot reveals a negative trend between 2006 and 2009 and a positive trend from 2009 to 2012. Twelve-month differencing yields a series, SDNODP, with an overall positive trend. Non-seasonal differencing of SDNODP yields a series, DSDNODP, with an overall horizontal trend. The correlogram of DSDNODP reveals a seasonality of period 12 months and the involvement of a seasonal moving average component of order one. The significant spikes of the autocorrelation function at lags 1 and 12 suggests an autocorrelaton structure of a (0, 1, 1)x(0, 1, 1)12 SARIMA model. This is hereby proposed, fitted and found to be adequate using a variety of arguments.
Time-plot of monthly Central African Franc (CFAFr or XAF) and Nigerian Naira (NGN) exchange rates... more Time-plot of monthly Central African Franc (CFAFr or XAF) and Nigerian Naira (NGN) exchange rates from January 2004 to January 2017 shows a slight positive trend up to May 2016 after which there is an abrupt astronomical rise which calls for intervention. The intervention point is therefore June 2016 around which time the Nigerian economy sank into recession. Â At 1% level of significance the pre-intervention rates are non-stationary and differencing the series once renders it stationary. Â This pre-intervention series has the autocorrelation structure of white noise. This white noise model structure is confirmed by a non-significant ARIMA (6,1,6) fit. Â Post-intervention forecasts are obtained on the basis of the pre-intervention white noise model. Â The difference between post-intervention forecasts and actual observations is modelled to obtain the intervention model. The intervention model is statistically significant and may be useful as basis for intervention in the circumstance.
Martinez, et al. [1] analysed monthly numbers of dengue cases as reported in Campinas, southeast ... more Martinez, et al. [1] analysed monthly numbers of dengue cases as reported in Campinas, southeast Brazil from 1998 to 2008, by SARIMA methods. Assuming X is the original series, they analysed the logarithm of X + 1. The models they proposed and compared are of orders (2,1,2)x(1,1,1)12, (2,1,1)x(1,1,1)12, (1,1,2)x(1,1,1)12, (1,1,1)x(1,1,1)12, (2,1,3)x(1,1,1)12, and (1,1,3)x(1,1,1)12. Using the R software, they chose the SARIMA(2,1,2)x(1,1,1)12 model as the best on the basis of Akaike information criterion, AIC. The result in this work is different: the SARIMA(2,1,1)x(1,1,1)12 model is herein adjudged as the best on the same minimum AIC grounds.
The daily exchange rates of the Nigerian Naira (NGN) and Malaysian Ringgit (MYR) from Wednesday,6... more The daily exchange rates of the Nigerian Naira (NGN) and Malaysian Ringgit (MYR) from Wednesday,6 th November 2013 to Monday, 21 st April 2014 are being modeled by Seasonal Autoregressive Integrated Moving Average (SARIMA) methods. The realization herein referred to as RNER initially had a downward trend to January 2014 after which the trend became positive. That means that initially the Naira appreciated before depreciating relatively after January. A 7-day differencing of RNER produced the series called SDRNER with a fairly horizontal trend. The Augmented Dickey Fuller (ADF) Test declares RNER and SDRNER as non-stationary and stationary respectively. The correlogram of SDRNER has an autocorrelation function (ACF) that cuts off at lag 4 and a partial autocorrelation function (PACF) that cuts off at lag 1 suggesting a SARIMA (1, 0, 4)x(0, 1, 0)7 model fit. The residuals of this model, rather than being uncorrelated, are seasonal with period 7. This seems to invalidate the model. A f...
Many economic and business time series exhibit seasonal tendencies. Analytical techniques for suc... more Many economic and business time series exhibit seasonal tendencies. Analytical techniques for such series which take into account these tendencies have engaged the attention of researchers of recent. One such modelling technique is the Box-Jenkins seasonal autoregressive integrated moving average (SARIMA) technique. A novel algorithm is hereby proposed. This algorithm which is based on autoregressive-moving average duality arguments is applied to model daily exchange rates of the British pound sterling and the European Euro currencies. The data analyzed are 178 daily pound/euro exchange rates 13 th December 2015 to 7 th June 2016. Application of the algorithm using the SARIMA(1,1,1)x(1,1,1) 7 template as proposed yields a SARIMA(1,1,1)x(0,1,1) 7 model. Further 8 values from 8 th June to 15 th June 2016 are used for out-of-sample comparison of observations with forecasts. The adequacy of the chosen model is not in doubt since the residuals are uncorrelated and are normally distribute...
Am 10.12.2019 ist der langersehnte Referentenentwurf eines Gesetzes zur Umsetzung der Anti-Steuer... more Am 10.12.2019 ist der langersehnte Referentenentwurf eines Gesetzes zur Umsetzung der Anti-Steuervermeidungsrichtlinie (ATAD-Umsetzungsgesetz – ATADUmsG) veröffentlicht worden, diesmal sogar „offiziell“. Der Beitrag versteht sich insoweit als „Update“ zu dem bereits von Haase/Hofacker besprochenen „inoffiziellen“ Gesetzesentwurf vom Dezember 2018 (Ubg 2019, 260). Vorliegend werden zur Vermeidung von Wiederholungen nur die Änderungen gegenüber dieser „Kleinen Lösung“ herausgearbeitet, die sich zwar vom Umfang her im Rahmen halten, aber dem Rechtsanwender dennoch Überraschendes bieten. Der Beitrag wird abgerundet durch Kurzhinweise zu nun erstmals bekanntgewordenen Neuerungen im Anwendungsbereich der §§ 1 und 6 AStG sowie zur Neueinführung eines § 4k EStG. Der ursprünglich sehr kurzfristig für den 18.12.2019 geplante Kabinettsbeschluss wurde gleichsam „in letzter Sekunde“ wieder abgesagt und in das neue Jahr vertagt. Hoffentlich nimmt der Gesetzgeber die gewonnene Zeit zum Anlass, das Gesetz noch einmal inhaltlich zu überdenken.
Rainfall is natural climatic phenomena whose prediction is challenging and demanding. Worldwide n... more Rainfall is natural climatic phenomena whose prediction is challenging and demanding. Worldwide numerous attempts have been made to predict its behavioral pattern using various techniques. The present study is to find a suitable seasonal forecasting model for forecasting monthly rainfall in Tamilnadu. For this purpose, a dataset containing a total of 136 years (1871-2006) monthly rainfall totals of Tamilnadu is obtained from Indian Institute of Tropical Meteorology (IITM), Pune, India and the suitable forecasting model is identified through Box-Jenkins SARIMA modeling.
This research is about an intervention on daily exchange rates of the Nigerian Naira (NGN) and it... more This research is about an intervention on daily exchange rates of the Nigerian Naira (NGN) and its Ugandan counterpart, the Shilling (UGX) observed on 22 nd June 2016. The realization of this time series studied spans from 19 th May 2016 to 17 th November 2016. There is an abrupt jump in the amount of Naira exchanged for a shilling from 0.0509 to 0.0609 from 20 th June to 21 st June 2016 and then to 0.0840 the next day. Instead of coming down it has been moving up. The proposal of an intervention or interrupted time series model to explain this trend of events is the aim of this work. The pre-intervention exchange rates show an initial downward trend up to 26 th May 2016 and then an upward trend. They are adjudged to be non-stationary by the Augmented Dickey Fuller (ADF) test, necessitating their first order differencing. These differences are now stationary and are observed to have a random error fit. Post-intervention forecasts are made on the basis of this pre-intervention model....
A look at the time plot of daily amounts of British pound (GBP) per Euro (EUR) from 17 th as the ... more A look at the time plot of daily amounts of British pound (GBP) per Euro (EUR) from 17 th as the point of intervention. It is noteworthy that on the previous day 23 rd June 2016, the nation of Great Britain voted to opt out of European Union in what is known as Brexit. It is speculated here that this observed relative depreciation of the GBP is caused by this Brexit event. This work is aimed at studying this intervention situation. The pre-intervention exchange rates are adjudged to be non-stationary. Non-seasonal differencing makes it stationary and these differences have the autocorrelation structure of a white noise process. Post-intervention forecasts on the basis of this model are obtained and differences between these and the actual post-intervention observations are modeled for the intervention transfer function. The overall intervention model is observed to be significant and to agree closely with the actual observations. Out-of-sample forecasts comparison shows that forecas...
Journal of the Nigerian Association of Mathematical Physics, 2009
The efficiencies of eight autoregressive model order determination criteria: AIC, BIC, SIC, S, F,... more The efficiencies of eight autoregressive model order determination criteria: AIC, BIC, SIC, S, F, FPE4, CAT2, CAT3, for the selection of subset models are compared using artificial and real series. Our observation is that BIC, S and FPE4 performed well in a wide range of models.
Many economic and business time series exhibit seasonal tendencies. Analytical techniques for suc... more Many economic and business time series exhibit seasonal tendencies. Analytical techniques for such series which take into account these tendencies have engaged the attention of researchers of recent. One such modelling technique is the BoxJenkins seasonal autoregressive integrated moving average (SARIMA) technique. A novel algorithm is hereby proposed. This algorithm which is based on autoregressive-moving average duality arguments is applied to model daily exchange rates of the British pound sterling and the European Euro currencies. The data analyzed are 178 daily pound/euro exchange rates 13 th December 2015 to 7 th June 2016. Application of the algorithm using the SARIMA(1,1,1)x(1,1,1)7 template as proposed yields a SARIMA(1,1,1)x(0,1,1)7 model. Further 8 values from 8 th June to 15 th June 2016 are used for out-of-sample comparison of observations with forecasts. The adequacy of the chosen model is not in doubt since the residuals are uncorrelated and are normally distributed. ...
This is a study of the relative performance of nine automatic autoregressive order determination ... more This is a study of the relative performance of nine automatic autoregressive order determination criteria for full-order modeling using the least squares approach. Of the nine: AIC, FPE, CAT 2 , S, FPE4, Φ, SIC, BIC and CAT 3 , we have found the trio, AIC, FPE and CAT 3 , to be the most consistent. The rest underestimate relatively. Journal of the Nigerian Association of Mathematical Physics , Volume 15 (November, 2009), pp 117 – 122
A realisation, TBR, of Nigeria Treasury Bill Rates from January 2006 to December 2014 is analysed... more A realisation, TBR, of Nigeria Treasury Bill Rates from January 2006 to December 2014 is analysed by seasonal ARIMA methods. The time plot of the realisation reveals an overall downward trend from 2006 to 2009 followed by an overall upward trend up to 2013. Twelve-monthly differencing of TBR yields the series SDTBR which has an overall upward trend. Nonseasonal differencing of SDTBR yields the series DSDTBR with an overall horizontal trend and no clear seasonality. By the Augmented Dickey-Fuller Unit Root Test both TBR and SDTBR are adjudged non-stationary whereas DSDTBR is adjudged stationary. The correlogram of DSDTBR has a negative significant spike in the autocorrelation function at lag 12, an indication of seasonality of period 12 months and the presence of a seasonal moving average component of order one. By a novel proposal credited to Suhartono, initially the (0, 1, 1)x(0, 1, 1)12 SARIMA model is fitted. The non-significance of the lag 13 coefficient suggests the additive SA...
This work is a time series analysis of the monthly domestic consumption of Nigerian Petroleum pro... more This work is a time series analysis of the monthly domestic consumption of Nigerian Petroleum products. The realization analyzed is a 110-point series which spans from July 2006 to August 2015. A time plot of the data shows a generally downward trend. Even though the Augmented Dickey Fuller Unit Root Test is significant, the series could not be said to be stationary because its correlogram reveals an underlying trend and a 12 monthly seasonality. A seasonal difference of the series shows no trend. Its correlogram is suggestive of a seasonal autoregressive integrated moving average (SARIMA) model of order (0,0,1)x(1,1,1) . Diagnostic checking 12 confirms its adequacy. For instance its residuals are largely uncorrelated and are normally distributed. Forecasting and simulations of the monthly domestic consumption quantities could therefore be done using the model.
A brief history of the exchange rates between the Uganda shilling and the United States dollars i... more A brief history of the exchange rates between the Uganda shilling and the United States dollars is given. Moreover, this work involves modeling of their monthly exchange rates by seasonal Box-Jenkins methods. Clearly with time more shillings are exchanged for the dollar, an evidence of relative depreciation of the shilling. An inspection of a realization of the time series which covers from July 1990 to November 2014 reveals a 12-monthly seasonality. A 12-monthly seasonal differencing and then a non-seasonal differencing of the seasonal differences is enough to rid the series of non-stationarity. The autocorrelation structure of the resultant series suggests two seasonal autoregressive integrated moving average (SARIMA) models of orders: (0, 1, 1)x(0, 1, 1)12 and (0, 1, 1)x(1, 1, 1)12. Diagnostic checking shows that the former is the more adequate on all counts. It is therefore recommended that forecasting of the series be based on it.
The time plot of the series NEER shows an overall positive trend with a peak in early 2010 after ... more The time plot of the series NEER shows an overall positive trend with a peak in early 2010 after a deep depression in late 2008. No seasonality is discernible by this visual inspection. Seasonal (i.e. 12-month) differencing yields SDNEER which exhibits an overall slightly positive trend and a high peak in late 2009. Still the visual inspection of the time plot in Figure 2 hardly makes any seasonality obvious. A non-seasonal differencing of SDNEER yields DSDNEER with an overall horizontal trend. Though the time plot in Figure 3 does not give an impression of any regular seasonality, the correlogram of Figure 4 reveals seasonality of period 12 months. Besides there is indication that the product of two moving average components both of order one is involved: one component is seasonal and the other non-seasonal. In addition to that a significant spike of the partial autocorrelation function at lag 12 suggests the involvement of a seasonal autoregressive component of order one. Therefo...
The capital budgeting problem is a multi-constraint Knapsack problem. Hence this paper provides a... more The capital budgeting problem is a multi-constraint Knapsack problem. Hence this paper provides a solution to a capital budgeting problem of Akwa Ibom State, Nigeria using a Branch and Bound approach. The capital projects are summarized in four broad groups: The Economic sector ( ) x , The Social Service sector ( ) x , The Environmental/Regional Development sector ( ) x , and The Administration sector ( ) x . Using Tora software (version 11) for the analysis, it was observed that the optimal solution was found in node 60 while the upper bound and the lower bound were 154.46 and 129.76 respectively. The result shows that the second and the third sector will be selected
A 149-point realization of daily exchange rates of the Uganda shilling (UGX)-Nigerian naira (NGN)... more A 149-point realization of daily exchange rates of the Uganda shilling (UGX)-Nigerian naira (NGN) from 4 th October, 2014 to 1 st March, 2015, is analyzed by Box-Jenkins methods. By a new fitting algorithm, it is concluded that the time series follows the subset SARIMA (1,1,0)x(1,1,0) 7 model. Daily exchange rates between the two currencies may be simulated or forecasted by the model. Introduction Foreign exchange is a major issue in the discussion of world economy. Any trade relationship between the country Uganda and the country Nigeria is based on the relative value of the Uganda Shilling (UGX) and the Nigerian Naira (NGN). In this write-up the daily exchange rates shall be modelled by Box-Jenkins methods. The particular approach shall be the seasonal autoregressive integrated moving average (SARIMA) approach proposed by Box et al. [1]. In recent times, many authors have adopted the SARIMA modelling approach to model real life data. Jianfeng (2013) noticed that SARIMA modelling r...
We consider a dynamic stochastic knapsack problem with the aim of minimizing the cost of the sele... more We consider a dynamic stochastic knapsack problem with the aim of minimizing the cost of the selected items whose weights follow a mixture of Poisson and Exponential distribution using additive model. A graphical presentation of our contagious distribution with different values of both parameters and range of X is made to show their behaviors. We also propose an algebraic model for the problem.
Background: The Central Bank of Nigeria has itemized Nigerian real Gross Domestic Product (GDP) i... more Background: The Central Bank of Nigeria has itemized Nigerian real Gross Domestic Product (GDP) into the following: crop production, livestock, forestry, fishing, crude petroleum and natural gas, solid minerals, manufacturing, construction, trade, transport, information and communication, utilities, accommodation and food services, finance and insurance, real estate, professional, scientific and technical services, administrative, support and business services, public administration, education, human health and social services, arts, entertainment and recreation and other services. Objective: This paper is an attempt to break Nigerian real GDP into clusters on the basis of their contributions in the year 2018 and the first three quarters of 2019. Methodology: The researcher made use of a combination of two distances: (i) the Pearson’s (correlation coefficient) distance and (ii) the absolute correlation coefficient distance to assist into breaking Nigeria’s GDP into clusters. Addi...
A realization of monthly Nigerian crude oil domestic production, NODP, from January 2006 to Augus... more A realization of monthly Nigerian crude oil domestic production, NODP, from January 2006 to August 2012, is analyzed. The time plot reveals a negative trend between 2006 and 2009 and a positive trend from 2009 to 2012. Twelve-month differencing yields a series, SDNODP, with an overall positive trend. Non-seasonal differencing of SDNODP yields a series, DSDNODP, with an overall horizontal trend. The correlogram of DSDNODP reveals a seasonality of period 12 months and the involvement of a seasonal moving average component of order one. The significant spikes of the autocorrelation function at lags 1 and 12 suggests an autocorrelaton structure of a (0, 1, 1)x(0, 1, 1)12 SARIMA model. This is hereby proposed, fitted and found to be adequate using a variety of arguments.
Time-plot of monthly Central African Franc (CFAFr or XAF) and Nigerian Naira (NGN) exchange rates... more Time-plot of monthly Central African Franc (CFAFr or XAF) and Nigerian Naira (NGN) exchange rates from January 2004 to January 2017 shows a slight positive trend up to May 2016 after which there is an abrupt astronomical rise which calls for intervention. The intervention point is therefore June 2016 around which time the Nigerian economy sank into recession. Â At 1% level of significance the pre-intervention rates are non-stationary and differencing the series once renders it stationary. Â This pre-intervention series has the autocorrelation structure of white noise. This white noise model structure is confirmed by a non-significant ARIMA (6,1,6) fit. Â Post-intervention forecasts are obtained on the basis of the pre-intervention white noise model. Â The difference between post-intervention forecasts and actual observations is modelled to obtain the intervention model. The intervention model is statistically significant and may be useful as basis for intervention in the circumstance.
Martinez, et al. [1] analysed monthly numbers of dengue cases as reported in Campinas, southeast ... more Martinez, et al. [1] analysed monthly numbers of dengue cases as reported in Campinas, southeast Brazil from 1998 to 2008, by SARIMA methods. Assuming X is the original series, they analysed the logarithm of X + 1. The models they proposed and compared are of orders (2,1,2)x(1,1,1)12, (2,1,1)x(1,1,1)12, (1,1,2)x(1,1,1)12, (1,1,1)x(1,1,1)12, (2,1,3)x(1,1,1)12, and (1,1,3)x(1,1,1)12. Using the R software, they chose the SARIMA(2,1,2)x(1,1,1)12 model as the best on the basis of Akaike information criterion, AIC. The result in this work is different: the SARIMA(2,1,1)x(1,1,1)12 model is herein adjudged as the best on the same minimum AIC grounds.
The daily exchange rates of the Nigerian Naira (NGN) and Malaysian Ringgit (MYR) from Wednesday,6... more The daily exchange rates of the Nigerian Naira (NGN) and Malaysian Ringgit (MYR) from Wednesday,6 th November 2013 to Monday, 21 st April 2014 are being modeled by Seasonal Autoregressive Integrated Moving Average (SARIMA) methods. The realization herein referred to as RNER initially had a downward trend to January 2014 after which the trend became positive. That means that initially the Naira appreciated before depreciating relatively after January. A 7-day differencing of RNER produced the series called SDRNER with a fairly horizontal trend. The Augmented Dickey Fuller (ADF) Test declares RNER and SDRNER as non-stationary and stationary respectively. The correlogram of SDRNER has an autocorrelation function (ACF) that cuts off at lag 4 and a partial autocorrelation function (PACF) that cuts off at lag 1 suggesting a SARIMA (1, 0, 4)x(0, 1, 0)7 model fit. The residuals of this model, rather than being uncorrelated, are seasonal with period 7. This seems to invalidate the model. A f...
Many economic and business time series exhibit seasonal tendencies. Analytical techniques for suc... more Many economic and business time series exhibit seasonal tendencies. Analytical techniques for such series which take into account these tendencies have engaged the attention of researchers of recent. One such modelling technique is the Box-Jenkins seasonal autoregressive integrated moving average (SARIMA) technique. A novel algorithm is hereby proposed. This algorithm which is based on autoregressive-moving average duality arguments is applied to model daily exchange rates of the British pound sterling and the European Euro currencies. The data analyzed are 178 daily pound/euro exchange rates 13 th December 2015 to 7 th June 2016. Application of the algorithm using the SARIMA(1,1,1)x(1,1,1) 7 template as proposed yields a SARIMA(1,1,1)x(0,1,1) 7 model. Further 8 values from 8 th June to 15 th June 2016 are used for out-of-sample comparison of observations with forecasts. The adequacy of the chosen model is not in doubt since the residuals are uncorrelated and are normally distribute...
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