S M O O T H I N G T E C H N I Q U E S

TIME SERIES

COMPONENTS OF A TIME SERIES

Components of a time series• Seasonal effect• Long term trend• Cyclical effect• Irregularity, random variation or random error

SEASONAL EFFECT

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)

LONG TERM TREND

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

RANDOM/ IRREGULAR COMPONENT

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.

CYCLICAL EFFECT

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.

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 ).

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. 

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)

 

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

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.

CALCULATING AVERAGE SEASONAL EFFECT

effectsseasonalofnumber

effectsseasonalindividualsumEffectSeasonalAverage

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