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Lecture 8

# Lecture 8 - Topics Econ1320 Lecture 8 Time Series B...

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1 1 Econ1320 Lecture 8 - Time Series B Sections 16.1, 16.4 & 16.5 2 Topics square6 Moving average- Smoothing square6 Deseasonalising square6 Autoregression (AR) model square6 Selecting a forecasting model square6 Out of sample prediction 3 Recall Lecture 7 square6 There are possible up to four components in a time series: trend, cycles, seasonal effects & irregular fluctuation square6 Stationary time series data does not contain trend, cyclical or seasonal effects. square6 Data plot can be used to see if the series has any patterns of these components. square6 Smoothing-out forecasting models can be used for stationary data. square6 Trend models can be used for data that does not have cyclical and seasonal effects. square6 If the data has cyclical and seasonal components barb4right can be removed. 4 Moving average- smoothing square6 We can smooth out the effect of any cyclical (or irregular) component by moving average smoothing. square6 Moving average smoothing replaces each observation Y t with an average of Y t and some of its adjacent values. square6 E.g. square6 The results depend on the choice of n : the MA gets smoother as n increases. 3 ) 3 ( 1 1 + - = t t t x x x MA 5 ) 5 ( 2 1 1 2 + + - - = t t t t t x x x x x MA 5 Excel & KADD square6 KADD/Forecasting/Moving Averages ring2 Select “ smoothing” ring2 For even n numbers barb4right manual square6 Excel/Tools/Data Analysis/Moving Averages 6 Example: QLD dwellings 10.5 11 11.5 12 12.5 13 13.5 14 14.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Actual 3-Period MA 5-Period MA

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2 7 Moving average- smoothing (cont.) square6 If n is an even number the uncentred MA must be “centred”. square6 Uncentred Centred square6 When smoothing out a cyclical component, n should be a multiple of the estimated average length of the cycle. 4 1 1 2 1 + - - + + + = t t t t x x x x s 4 2 1 1 2 + + - = t t t t x x x x s 2 x 2 1 t s s smoothed = 8 Example: QLD dwellings 12.1130 17 12.4463 12.5300 16 12.4306 12.4463 12.4150 12.2840 15 12.3376 12.4150 12.2603 12.8580 14 12.2655 12.2603 12.2708 11.9880 13 12.1676 12.2708 12.0645 11.9110 12 12.1756 12.0645 12.2868 12.3260 11 12.3703 12.2868 12.4538 12.0330 10 12.6684 12.4538 12.8830 12.8770 9 13.0061 12.8830 13.1293 12.5790 8 13.1344 13.1293 13.1395 14.0430 7 13.0879 13.1395 13.0363 13.0180 6 12.8851 13.0363 12.7340 12.9180 5 12.6246 12.7340 12.5153 12.1660 4 12.4054 12.5153 12.2955 12.8340 3 12.2955 12.1430 2 12.0390 1 MA(4) s2 s1 Actual Period 9 Deseasonalising square6 The method used to remove the seasonal effect is called ratio-to-moving-average method. square6 This method assumes a multiplicative model Y t = T · C · S · I where: T = trend - C = cyclicality S = seasonality - I = irregularity square6 SI = TCSI / TC square6 Where TC is the centred moving averages. square6 The average value of these ratios (TCSI/TC) is called seasonal indexes. square6 A method of eliminating the irregular fluctuation (I) can be applied, leaving only the seasonal effect (S). square6 Deseasonalised series is the ratio of actual over its seasonal index 10 A step-wise procedure square6 Y t = T · C · S · I square6 Compute the moving average (must centre if n is even) barb4right TC square6 Compute the ratio of actual to moving average barb4right SI t = Y t /TC square6
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Lecture 8 - Topics Econ1320 Lecture 8 Time Series B...

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