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The relationship between exchange rates and stock prices



The relationship between exchange rates and stock prices

Aim and objective

The aim of this project is to apply appropriate time series forecasting methods in order to help the management of the company to choose an appropriate forecasting model that could be used to predict stock prices in the short term with a reasonable level of accuracy.

Discussion

Autoregressive Integrated Moving Average (ARIMA) model was introduced by Box and Jenkins (hence also known as Box-Jenkins model) in 1960s for forecasting a variable. An effort is made in this paper to develop an ARIMA model for Total exchange rate quarter and to apply the same in forecasting Total stock prices for the three leading years. ARIMA method is an extrapolation method for forecasting and, like any other such method, it requires only the historical time series data on the variable under forecasting (Abry, 1994). Among the extrapolation methods, this is one of the most sophisticated methods, for it incorporates the features of all such methods, does not require the investigator to choose the initial values of any variable and values of various parameters a priori and it is robust to handle any data pattern. As one would expect, this is quite a difficult model to develop and apply as it involves transformation of the variable, identification of the model, estimation through non-linear method, verification of the model and derivation of forecasts. In what follows, we first explain the ARIMA model, then develop the same for Total stock prices using quarterly data during 1989 to 2007 and finally apply the same to forecast the values of the variable during the future 3 years. 

Model 1: ARIMA (1, 1, 1)

RIMA model, in theory, the most general class of models for forecasting time series that can be stationarized transformations such as differencing and logging. In fact, the easiest way to think of an ARIMA model as the modified version of random walks and random trend models: fine tuning consists of adding Lags of the difference of the series and / or Lags forecast error for the prediction equation, as necessary, to remove the last traces of autocorrelation of prediction error.

The acronym ARIMA stands for "Auto-Regressive Integrated Moving Average." Lags of the difference of the series, appearing in the equation predicting called "Auto-regressive" terms, lags behind the prediction error is called "moving average" conditions, and time series, which should be the difference to be made stationary is called "integrated" version of the stationary series. Random walks and random trend models, autoregressive model and exponential smoothing model (exponentially weighted moving averages) all special cases of model ARIMA.

"ARIMA(p,d,q)" model, where:

p is autoregressive terms,d is nonseasonal differences, and q is lagged forecast errors in the prediction equation.

Final Estimates of Parameters

Type Coef SE Coef T P

AR 1 -0.2451 0.6873 -0.36 0.723

SAR 4 0.1877 0.1699 1.10 0.273

MA 1 -0.0612 0.7128 -0.09 0.932

SMA 4 0.9121 0.0990 9.21 0.000

Constant -0.2756 0.2847 -0.97 0.337

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48

Chi-Square 4.6 13.2 25.7 36.6

DF 7 19 31 43

P-Value 0.713 0.827 0.737 ...