What Does Physics Teach Us?

There is an upward trend in the data, and returns increase gradually over time.

The spikes shown on the graph indicate a significant degree of seasonality.

To fit data, use exponential smoothing. Based on the variance you observe in the data, choose an appropriate constant. Comment on whether exponential smoothing is acceptable for this batch of data. Plot the model’s predictions alongside the initial data on the graph. How well does this technique fit the data? Create predictions for 1997. The most appropriate constant for smoothing is a number close to one since there is high seasonality in data as shown in the graph above in number 1. Hence my choice for the constant as provided for by solver in excel is 0.8. The appropriateness of exponential smoothing in representing data from the given time series is optimal since it tries to smoothen the graph as progression of data undertakes over time for better presentation.

Exponential smoothing formula

Mean Absolute Percentage Error 9.019

QN. 3

Use regression to build a linear trend model. Comment on the goodness-of-fit of this model to the data (or, how well does R2 explain the variance in the data?). Plot the predictions from this model on the graph with the original data.

The graph above is a representation of the given data and its representation by Gretl

Regression by using linear model fits information well on the graph hence is appropriate for a confident presentation of data.

QN.4

Develop multiplicative seasonal indices for the linear trend model developed in question 3. Use these indices to adjust predictions from the linear trend model from question 3 above for seasonal effects. Plot the predictions from this model on the graph with the original data. How well does this technique fit the data? Make forecast for the next 12 months of 1997using this technique.

GRETL screen shot

boxreturns prediction std. error 95% interval

1997:01 147.00 147.32 15.689 116.25 - 178.38

1997:02 147.00 149.41 15.689 118.34 - 180.47

1997:03 146.00 150.05 15.689 118.98 - 181.11

1997:04 136.00 147.50 15.689 116.43 - 178.57

1997:05 146.00 148.50 15.689 117.43 - 179.57

1997:06 142.00 184.23 15.689 153.16 - 215.29

1997:07 181.00 173.59 15.689 142.53 - 204.66

1997:08 179.00 162.95 15.689 131.89 - 194.02

1997:09 161.00 152.32 15.689 121.25 - 183.38

1997:10 127.00 159.41 15.689 128.34 - 190.47

1997:11 136.00 158.23 15.689 127.16 - 189.29

1997:12 167.00 177.41 15.689 146.34 - 208.47

Forecast evaluation statistics

Mean Absolute Percentage Error 8.581

QN. 5

Which forecasting methods of those that you tried do you think have the most confidence in making accurate forecasts for 1997? Use MAPE as you criterion to justify your decision.

MAPE formula

Using this criterion and the forecastic statiscics from Gretl which have given us the MAPE output for each technique used the best criterion is linear regression.

REFRENCE

Application used Gretl