Measuring Forecast Performance of ARIMA Model:
An Application to U.S. Dollar/Bangladeshi Taka
Foreign Exchange Rate
Mohammad Khaleq Newaz
12 November, 2010.
• Effective management of foreign exchange is very
important to achieve tolerable inflation and a desired
level of economic growth for a country.
• It is crucial to forecast the exchange rate to evaluate
the benefits and risks attached to the international
Official Name : The People’s Republic of Bangladesh
Location & Borders : South Asia bordered by India on the east, west & north and by Bay of
Bengal on the south and small border strip with Myanmar on the
Area/Land : 147,570 square km-mostly alluvial fertile plain. Territorial Waters
22.22 km. Economic Zone up to 370.40 km. in the high seas, measured
from the base line.
Population/Literacy : 159.00 million (In 2007)/62.66% (In 2002)
Sectoral share of
: 21.91% agriculture, 28.44% industry, 49.65% service.
GDP/rate of growth : US$ 72.4 billion /6.2% (2007-08)
Per Capita GDP/GNI : US$554 / US$599 (2007-08)
: US$ 15.57 billion / US$ 21.44 billion (2008-2009)
: USA, EU countries, China, India, Pakistan, Japan, South Korea,
Canada, Australia, Malaysia, Hong Kong, Taiwan, Thailand,
Indonesia, Saudi Arabia and UAE
The existing studies (Hassani &
Zhigljavsky, 2010; Ayodeji,
2009; Maya & Gomez, 2008;
Pesaran & Pesaran, 2007;
Longmore & Robison, 2004) on
the forecasting exchange rate
have mostly based on advanced
The combination of these two factors has led to a plethora of work on
US$/BDT exchange rate.
There is the observation that
like all other financial markets
but perhaps to an even greater
degree, the market for foreign
exchange has large temporal
variations in volatility.
Objective of the study
To investigate which model (ARIMA, exponential
smoothing or naive 1) is superior in terms of predictive
power of US$/BDT exchange rates.
• Source: International Financial Statistics (IFS), monthly
publication by the IMF.
• Duration : From 1972 till to date
(From 1973M1 up to and including 2007M12 will be used for model
quantification and statistical verification. The remaining three years i.e.
2008M1 to 2010M4 observations in the sample held back for the
purpose of out-of-sample forecast evaluation).
• Frequency: Monthly
• Sample size : 432
• ARIMA (Autoregressive Integrated Moving Average):
Autoregressive – future values depend on previous values of the data
Moving average – future values depend on previous values of the errors
Integrated – refers to differencing the data
• Exponential smoothing : Forecast this month equals last month’s forecast
plus a proportion of the forecast error last month.
• Naive 1 or no change model : The Naїve1 or no change model assumes
that a forecast of a series at a particular period equals the actual value at
the last period available
• MAPE (Mean absolute percentage error) has
been used as a measure of forecasting accuracy because
this accuracy criterion has the advantage of being
measured in unit-free terms (Witt & Witt, 1991).
A plot of 1st difference of US$/BDT exchange
rate over time
US$/BDT exchange rate over time
Results and discussions
**H0: The possess a unit root / the data are not trend stationary
Currency Test for unit root in - ADF* PP* Ng.
US $/BDT Level 0.9951 0.9941 1.82970
1st Difference 0.0000 0.0000 -202.18
*Sig at < 0.05, ** MZa value (– 8.100, at 5% level)
Unit root test result
Model Constant MA(1)
(0,1,1) (0,0,0) with constant
Model 𝛂 γ δ
Winters’ additive 1.000 0.001 0.001
Comparison of models
Smoothing Naïve 1
Model (0,1,1) (0,0,0) with constant Winters’ additive No change model
MAPE 1.031% 1.054% 6.1571%
Ranking 1 2 3
A plot of observed and forecasted of US$/BDT exchange rate over time
• The main contribution of this study is evaluating the
forecast performance of the various time series models in a
comprehensive and systematic way.
• Empirical results in this study will also pave the way for
• It has been observed in the literature that several models are widely used
by academics and practitioners to forecast exchange rate.
• Nowadays there is no consensus about which method is superior in terms
of forecasting accuracy (Poon and Granger, 2003; Taylor, 2005; Andersen et
al., 2006). Some authors conclude that time series forecasting models are
superior (Engle, 1982; Bollerslev, 1986). Other studies (i.e. Benavides &
Capistran, 2009) argue that the combination of the models can yield better
results. Thus, the future study will be concentrate on “combination
forecasts” method instead of forecasts made by individual model.
Limitations and further work