smoothing techniques time series. components of a time series components of a time series seasonal...
TRANSCRIPT
![Page 1: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/1.jpg)
S M O O T H I N G T E C H N I Q U E S
TIME SERIES
![Page 2: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/2.jpg)
COMPONENTS OF A TIME SERIES
Components of a time series• Seasonal effect• Long term trend• Cyclical effect• Irregularity, random variation or random error
![Page 3: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/3.jpg)
SEASONAL EFFECT
![Page 4: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/4.jpg)
SEASONAL EFFECT
Seasonal variation• Regular period usually based on calendar.• Could be literally seasonal but may be monthly,
daily, does not have to related to the seasons (summer, autumn etc)
![Page 5: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/5.jpg)
LONG TERM TREND
![Page 6: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/6.jpg)
LONG TERM TREND
Long term trend• The most, slowly changing component• The long term component, either upward or
downward direction or stationary.• Rate of change• Due to long term changes such as population
growth or change, technological change
![Page 7: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/7.jpg)
RANDOM/ IRREGULAR COMPONENT
![Page 8: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/8.jpg)
RANDOM/ IRREGULAR COMPONENT
Random/ Irregular component• Most rapidly changing component• Totally unpredictable• What is left over after other components have
been taken out• Look for ramps, spikes, troughs etc.
![Page 9: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/9.jpg)
CYCLICAL EFFECT
![Page 10: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/10.jpg)
CYCLICAL EFFECT
Cyclical variation• The next most slowly changing component• Recurrent, wave-like changes in the series• The period and amplitude of the wave are not
predictable• Often due to the business cycle, prosperity,
recession, depression and recovery.
![Page 11: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/11.jpg)
SMOOTHING TECHNIQUES
• Often it is hard to see the trend of data because of random fluctuations. Getting rid of these bumps or noise helps to “smooth” the data, summarise it and reveal the long term trend. One way to do this is to work out the Moving Means
• Moving Means are easy to calculate. All data contributes to the mean, so an extreme piece of data can causes the moving mean to fluctuate dramatically.
• Choosing the order - The most effective approach in smoothing raw data by using moving averages method, is making the order the same number as there are intervals within the seasonal cycle for the data (e.g. monthly – order 12, seasons – order 4, daily - order 7, weekdays – order 5 ).
![Page 12: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/12.jpg)
TREND
After we have smoothed the data, a better approximation of the overall trend will be given by the graph.
If the smoothed graph is a horizontal line then the overall trend is to stay constant/stationary.
![Page 13: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/13.jpg)
TREND
If the smoothed graph is best approximated by a straight line then the trend is a constant addition (or subtraction) each complete cycle. That is, the change (e.g. profit or loss) is consistent each cycle.
• If the smoothed graph is best approximated by a curve then the trend is a multiplier (e.g. inflation)
![Page 14: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/14.jpg)
TREND
If the smoothed graph is best approximated by a curve then the trend is a multiplier (e.g. inflation)
The two types of model• The additive model is suitable where the periodic
variation is of constant magnitude• The multiplicative model is suitable where the
periodic variation is of increasing magnitude
![Page 15: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/15.jpg)
CALCULATING SEASONAL EFFECTS
INDIVIDUAL SEASONAL EFFECT = RAW VALUE – MOVING MEAN
It gives a value to how much the raw data is above or below the smoothed data value so some seasonal effects will be negative.
![Page 16: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/16.jpg)
CALCULATING AVERAGE SEASONAL EFFECT
effectsseasonalofnumber
effectsseasonalindividualsumEffectSeasonalAverage
![Page 17: SMOOTHING TECHNIQUES TIME SERIES. COMPONENTS OF A TIME SERIES Components of a time series Seasonal effect Long term trend Cyclical effect Irregularity,](https://reader036.vdocuments.net/reader036/viewer/2022062407/56649da05503460f94a8c6a1/html5/thumbnails/17.jpg)
SEASONALLY ADJUSTING DATA
If we want to remove the seasonality of the data that we are measuring then we need to calculate the seasonally adjusted data.
Seasonally adjusted values (SAV) are raw data values with the seasonal effect removed, i.e.
SAV = RAW – ASE