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Volume 6,Issue 4,July - Aug.,2019


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Daily British Pound and US Dollar Exchange Rates Modelling by Seasonal Box-Jenkins Methods

  • Etuk, Ette Harrison
  • Chims, Benjamin Ele
A SARIMA model for forecasting daily exchange rates of the British Pound (GBP) and the United States Dollars (USD) is proposed and fitted. The realization spans from 5th February 2014 to 16th October 2014. The time plot of the series called herein PDER shows an initial upward trend up to Saturday 5th July followed by a downward trend. This means that prior to 5th July the dollar depreciated relatively after which it appreciated. A seven-day differencing of PDER yields a series herein called SDPDER exhibiting a generally horizontal trend. The Augmented Dickey Fuller unit root test adjudges PDER as non-stationary and SDPDER as stationary. However the correlogram of SDPDER shows evidence of non-stationarity in the series. A non-seasonal differencing of SDPDER yields the series DSDPDER which also exhibits a horizontal secular trend. It is certified as stationary by the unit root test. Its correlogram shows an autocorrelation structure of a stationary series. Moreover there is an indication of seasonality of period 7 days and the involvement of seasonal autoregressive (AR) and moving average (MA) components order one each. Taking into consideration the duality of AR and MA models suggestive models include (1) A Sarima (0, 1, 1)x(0, 1, 1)7 and (2) A Sarima (0, 1, 0)x(1, 1, 1)7. On Akaike’s Information Criterion (AIC) grounds the latter model is the more adequate. This model further yields a more adequate model: Sarima(0, 1, 0)x(0, 1, 1)7. Therefore the proposed model is the Sarima(0, 1, 0)x(0, 1, 1)7. Its residuals are mostly uncorrelated indicating model adequacy. Forecasting of the exchange rates may be based on this model
Select Volume / Issue:
Year:
2014
Type of Publication:
Article
Keywords:
Foreign Exchange Rates; GBP; SARIMA Models; USD
Journal:
IJASM
Volume:
1
Number:
1
Pages:
5-8
Month:
Sept.- Oct.
ISSN:
2394-2894
Hits: 1313

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