Time Series Analysis Introduction Averaging Trend Seasonality.

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Presentation transcript:

Time Series Analysis Introduction Averaging Trend Seasonality

Lecture Objectives You should be able to : 1.Discuss the advantages and limitations of time series forecasting. 2.Use averaging, trend, and seasonality models appropriately. 3.Interpret the Bias, MAD, MAPE and Standard Error to evaluate a forecast.

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

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

Naive Forecast Naive PeriodSalesForecast 160N/A How good is this forecast?

Evaluating the Forecast XYNaive Abs PercentSquared PeriodSalesForecastError % % % % % % % % % %68.1 BIASMADMAPEMSE Standard Error (Square Root of MSE) =8.3 Error = Bias = Avg (Errors) MAD = Avg (Abs Errors) MAPE = Avg (Percent Errors) MSE = Avg (Squared Errors)

Moving Averages Moving Avg. Abs. PercentSquared PeriodSalesForecastError 160N/A 267N/A 350N/A % % % % % % % %29.86 BIASMADMAPEMSE Standard Error (Square Root of MSE) =5.5 How does this 3-period moving average forecast compare to the Naive forecast?

Simple Exponential Smoothing alpha=0.3 Exponential PercentSquared PeriodSalesSmoothingErrorAbs. ErrorError 1 60N/A % % % % % % % % % %42.79 BIASMADMAPEMSE Standard Error (Square Root of MSE) =6.5

Interpretation Bias – indicates the direction of the errors. On average, is the forecasting technique underestimating or overestimating? Bias can be corrected. MAD – The average magnitude 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.

Questions 1. Can Bias be greater than MAD? 2. If we know the Bias, can we figure out the MAD value? 3. Will Bias is lower for one technique than another, will MAD also be lower? 4. Answer the above questions for MSE and MAD instead of Bias and MAD.

Data with a Trend PeriodSales

Fitting a Trendline

Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations10 ANOVA dfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-valueLower 95% Intercept Period

Seasonality QuarterSales (Y) Is there a trend? Is there seasonality?

Deseasonalizing

Trend and Seasonally Adjusted Forecasts

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?