Time series using forecast accuracy and suitability of methods

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See the attached file.

Assignment - 1: Forecasting in Practice

Question 1:

The time series assigned to me for analysis and forecasting is MND21. This is a monthly time series starting from December 1977 and ending in October 1983. The underlying variable represented by the time series is DEMOGR, which indicates that it is some sort of demographic variable. The graphical presentation of the time series is as below:

The time series shows very high values and volatility for the period December 1977 to December 1979. During December 1979 to December 1980, we can call it is in transition phase where the time series is switching from high value and high volatility period to low value and low volatility period which starts from December 1980. Beyond December 1980, the time series enters in a phase of low volatility and low absolute values.

The descriptive statistics for the time series are presented below. To get a better understanding, the descriptive statistics for the three distinct phases of the time series are also presented.

Full Time Series High Period Transition Low Period
Dec'77 to Dec'79 Dec'79 to Dec'80 Dec'80 to Oct'83
Mean 270.03 666.56 163.92 20.71
Median 35.00 639.00 137.00 20.00
Mode 23.00 322.00 NA 26.00
Maximum 1216.00 1216.00 422.00 88.00
Minimum 8.00 307.00 23.00 8.00
Variance 110230.68 55365.01 15921.41 169.92
Standard Deviation 332.01 235.30 126.18 13.04
Skew 1.05 0.28 0.68 4.15
Kurtosis -0.13 0.00 -0.40 21.79

The descriptive statistics for the three distinct phases clearly indicated that there is structural break in the time series and any forecasting or econometric analysis for the time series should be done separately for the high and low periods for the time series. However, for the purpose of this assignment, I have assumed that there is no structural break in the time series and have gone ahead with forecasting by taking all the data points in the time series (however by withholding last 12 months data).

Selecting Error Measures:

Before forecasting the time series values for the last 12 months, it is important to decide which error measures should be selected to decide the best forecasting method. There are a large number of error measures available in theory. Broadly, we can categorize them into simple error measures, percentage error measures, cumulative error measures, mean error measures and mean percentage error measures.

The time series I am evaluating as part of this assignment has very high values at the beginning of the time series and small numbers towards the end of the time series. Therefore, the size or magnitude of the forecast variable is important in evaluating the accuracy of the forecast. For example, an error of 10 points when the actual value is 800 points is quite different from that when the actual value is just 10 points. Percentage based error measures provide an indication of how large the forecast errors are in comparison to the actual values of the series. For forecasting the time series for my assignment, percentage based error measures are likely to do a better job as compared to non-percentage based measures.

Within the percentage based measures, there are various options available for the error measures such as percentage error, mean percentage error, absolute percentage error, mean absolute percentage error, root in percentage of error and root of mean absolute percentage error. In case of simple percentage error or mean percentage error, the positive deviations and negative deviations cancel each other, hence if we are making large forecasting errors but making them on both sides of the actual value (positive and negative), we may end up getting very good performance on error metric but very poor forecasting results.

Absolute percentage error and mean absolute percentage error measures the forecast accuracy by taking the magnitude of the forecasting errors. These measures are more useful when we are interested in measuring the forecast errors in the same unit as the original series. Root square methods approach penalizes large forecasting errors since the errors are squared. This is important because a technique, which produces moderate errors, is preferable to one that usually has small errors but occasionally yields extremely large ones.

Based on above discussion and the properties of the time series I am evaluating, I decided to use the following three error measures for this assignment:
 Absolute percentage error
 Mean absolute percentage error
 Root of mean absolute percentage error

Selecting Forecasting Method:

Selection of appropriate forecasting technique for a time series depends upon several factors related to the forecasting such as why is forecast needed, how it will be used and characteristics of the data series. One of the major factors influencing the selection of a forecasting technique is the identification and understanding of the historical patterns in the data.

I tested 11 different forecasting techniques to ...