Time Series Analysis

1. Time Series Analysis Introduction Averaging Trend Seasonality

2. Lecture Objectives • You should be able to : • Discuss the advantages and limitations of time series forecasting. • Use averaging, trend, and seasonality models appropriately. • Interpret the Bias, MAD, MAPE and Standard Error to evaluate a forecast.

3. Basic Forecasting Process • Look at the data (Graph) • Forecast (choose one or more methods) • Evaluate (examine errors)

4. Time Series Sales Data Consider the following sales data for 10 time periods (quarters) What is a good forecast for Sales for the next period?

5. Naive Forecast How good is this forecast?

6. Evaluating the Forecast Error = Bias = Avg (Errors) MAD = Avg (Abs Errors) MAPE = Avg (Percent Errors) MSE = Avg (Squared Errors)

7. Moving Averages How does this 3-period moving average forecast compare to the Naive forecast?

8. Simple Exponential Smoothing

9. Interpretation Bias – indicates the direction of the errors. On average, is the forecasting technique underestimating or overestimating? Bias can be corrected. MAD – The averagemagnitude of error. MAPE – The average percent error. Error as a percent of the actual values of y. MSE – Mean Squared Error. SE – Square root of MSE. This is the standard deviation of the error terms. Useful for constructing confidence intervals.

10. Questions • Can Bias be greater than MAD? • If we know the Bias, can we figure out the MAD value? • Will Bias is lower for one technique than another, will MAD also be lower? • Answer the above questions for MSE and MAD instead of Bias and MAD.

11. Data with a Trend

12. Fitting a Trendline

13. Regression Output

14. Seasonality Is there a trend? Is there seasonality?

15. Deseasonalizing

16. Trend and Seasonally Adjusted Forecasts

17. Questions • How many seasons can there be in data? • How many seasonal cycles are needed to determine if seasonality exists? • What does a seasonal index of 1.2 mean?