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

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1 1 Econ1320 Lecture 8 - Time Series B 2 Topics s Moving average- Smoothing s Deseasonalising s Autoregression (AR) model s Selecting a forecasting model s Out of sample prediction 3 Recall Lecture 7 s There are possible up to four components in a time series: trend, cycles, seasonal effects & irregular fluctuation s Stationary time series data does not contain trend, cyclical or seasonal effects. s Data plot can be used to see if the series has any patterns of these components. s Smoothing-out forecasting models can be used for stationary data. s Trend models can be used for data that does not have cyclical and seasonal effects. s If the data has cyclical and seasonal components b can be removed. 4 Moving average- smoothing s We can smooth out the effect of any cyclical (or irregular) component by moving average smoothing. s Moving average smoothing replaces each observation Y t with an average of Y t and some of its adjacent values. s E.g. s 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 s KADD/Forecasting/Moving Averages r Select “ smoothing” r For even n numbers b manual s 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.) s If n is an even number the uncentred MA must be “centred”. s Uncentred Centred s 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 s The method used to remove the seasonal effect is called ratio-to-moving-average method. s This method assumes a multiplicative model Y t = T · C · S · I where: T = trend - C = cyclicality S = seasonality - I = irregularity s SI = TCSI / TC s Where TC is the centred moving averages. s The average value of these ratios (TCSI/TC) is called seasonal indexes. s
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This note was uploaded on 10/21/2009 for the course ECON 1320 taught by Professor John during the Three '08 term at Queensland.

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

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