Strategic Alliance: Arima Modelling

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MFEFM ASSIGNMENT

ARIMA Modelling

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Objective

The objective is to analyze the closing Prices of stock of ITC over the period 7-29-2015 to 9-28-2015 and forecast the same for the next 3 days.

ARIMA Modeling

Stage 1 - Identification

• Data Spreadsheet: Closing Prices of stock of ITC over the period 7-29-2015 to 9-28-2015 are imported and shown below.

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• Line graph of the Data set: Neither trends nor seasonality was visible; no conclusions were made about the same.

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• Correlogram of the data: There is no decaying trend in the correlogram. There might be seasonality in the data. AR(1) and MA(1) signatures can be seen.

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• Unit-root test:  We performed Unit root test to verify this. Selection of “Level” at “Trend & Intercept” gave the results shown below in which the t-statistic values at all three significance levels are more than the Augmented Dickey-Fuller test statistic, suggesting that the Null Hypothesis “CLOSE has a unit root” is rejected. This implied that the data does not have a trend.

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Stage 2 – Estimation

• Estimation of values of co-efficients – As there was no clear signature for seasonality in the data, we proceed with estimation. Using least square technique we estimated the following: ls d(close,1,0) c ar(1) ma(1)

This gave us the results shown below. AR(1) is significant at 5% level and MA(1) is significant at 5% level. So this is an AR(1) MA(1) process.

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Stage 3 – Diagnostic Checking

• Residual test: Now we will check for white noise process by taking the residual Q-statistics test. The residual test gave the above result where all p-values are >5%, except that at lag 3. However, as that value is 4.9%, which is very close to 5%, we will accept it. So we have reached the white noise process and no further information can be extracted from it. We now proceed for Static Forecasting.

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Stage 4 – Forecasting

• Forecasting: The following results were obtained for static forecasting for the last 5 days in the data set:

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The Static forecasting values are shown above in Gray Vs the actual values on the left.

The MAPE is as low as 0.819% suggesting that the model is good.

Now we will proceed to dynamic forecast, which gave the following results.

Now, we will also try de-seasonalizing the data to see which model is a better fit.

• De-seasonalizing: We use the following command to generate a new de-seasonalized series – series dd=d(close,0,5). The correlogram of the new series hence generated is given below, in which a clear ar(1) signature can be identified.

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• Estimation of values of co-efficients: Using least square technique we estimated the following: ls d(close,0,5) c ar(1). This gave us the results shown below. AR(1) is significant at 5% level. So this is an AR(1) process.

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• Residual test: Now we will check for white noise process by taking the residual Q-statistics test. The residual test gave the below result where all p-values are >5%. So we have reached the white noise process and no further information can be extracted from it.

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