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SESSION 53 - 56 Last Update 18 th June 2011 Time Series Forecasting.

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Presentation on theme: "SESSION 53 - 56 Last Update 18 th June 2011 Time Series Forecasting."— Presentation transcript:

1 SESSION 53 - 56 Last Update 18 th June 2011 Time Series Forecasting

2 Lecturer:Florian Boehlandt University:University of Stellenbosch Business School Domain:http://www.hedge-fund- analysis.net/pages/vega.php

3 Learning Objectives 1.Forecasting 2.Time Series Analysis 3.Time Series Forecasting – Linear Trend without Seasonality 4.Time Series Forecasting – Linear Trend with Seasonality

4 Forecasting - Methodologies Qualitative Methods: Here forecasting is based on intuition, estimates and opinions, typically from the sales force, customers or senior management. Such methods are frequently termed subjective or judgmental. Causal or Econometric Methods: Forecasting methods that establish causal relationships, such as in regression analysis. For example a motorcar manufacturer would base its demand forecasts on predictions of causal factors such as a) the interest rate, b) price of fuel, c) competitor pricing, d) business confidence indices, e) national income level, etc. Time Series Methods: These methods are based on the idea that prior occurrences can be used to predict the future, through a process of extrapolation.

5 Time Series Analysis - Definitions Time series analysis/decomposition breaks-down (decomposes) a time series into its constituent components in order to understand the structure of its pattern. There are four components to a time series: Secular trend (T) – underlying tendency for the time series to rise (or fall) over time. Seasonal variation (S) – regular rhythmic pattern e.g. month-end & Christmas sales. Cyclical variation (C) – a multi-year oscillation due to macro economic or industry level activity. Irregular variation (I) – unpredictable variations such as a plant breakdown, a strike, etc. These four components may possess an additive or multiplicative relationship:

6 Example Linear Trend – No Seasonality The table to the left displays the sales of Gold Tomato Sauce glass bottles in ‘000s. Is it possible to predict the future values of the time series for the year 2011 taking into consideration the past trend? The method employed is ignoring seasonal, cyclical or irregular variation. Yeary 200751 200868 200999 2010132 Total4350

7 Plotting Time Series

8 Guide to Time Series Forecasting excluding Seasonality 1.Set x values for each time period according to the zero-sum of x rules 2.Compute all x 2 and xy values and sum them 3.Find the equation of the line: a + b (x) 4.Use the result of step 3 to compute trend values for each time period 5.Set future values of x 6.Calculate y using the future value of x and equation a + b (x)

9 Step 1 + 2: Set x-Values and compute x 2 and xy Yearyxx^2xy 200751-39-153 2008681-68 20099911 201013239396 Total435020274 If n is even: If n is odd:

10 Step 3 + 4: Determine (T)rend (a+bx) (T)rend Yearyxx^2xya+bx 200751-39-15346.4 2008681-6873.8 20099911 101.2 201013239396128.6 Total435020274 a87.5 b13.7

11 Step 5 + 6: Set future values of x and estimate y-hat (T)rend Yearyxx^2xya+bx 200751-39-15346.4 2008681-6873.8 20099911 101.2 201013239396128.6 Total435020274 yx 20111565 a87.5 b13.7

12 Chart Forecast

13 Example Linear Trend - Quarterly Seasonality SALES TotalQuartery 19972653Q1210 Q2656 Q31319 Q4468 19983643Q1332 Q2988 Q31738 Q4585 19994769Q1461 Q21222 Q32272 Q4814 Total1211065 The table to the left displays an example for the quarterly values of a time series for three consecutive years. It is easy to see that the observed values fluctuate depending on the current quarter. Is it possible to predict the future values of the time series for the year 2000 taking into consideration the quarterly fluctuation? The method employed is ignoring cyclical or irregular variation.

14 Plotting Time Series

15 Guide to Time Series Forecasting including Seasonality 1.Set x values for each time period according to the zero-sum of x rules 2.Compute all x 2 and xy values and sum them 3.Find the equation of the line: a + b (x) 4.Use the result of step 3 to compute trend values for each time period 5.Compute the deviation of actual values from trend values (y / T) 6.Find the average deviation per time period (e.g. quarter). Adjust values to ∑= 4. 7.Set future values of x 8.Determine the future trend values 9.Input the seasonality values calculated in step 6 10.Finalise the sales forecast by multiplying the quarterly trend values by the quarterly seasonality values

16 Step 1 + 2: Set x-Values and compute x 2 and xy SALES TotalQuarteryixx^2xy 19972653Q12101-11121-2310 Q26562-981-5904 Q313193-749-9233 Q44684-525-2340 19983643Q13325-39-996 Q298861-988 Q31738711 Q45858391755 19994769Q146195252305 Q21222107498554 Q322721198120448 Q481412111218954 Total121106557221983 If n is even: If n is odd:

17 Step 3 to 5: Determine (T)rend (a+bx) and compute deviation SALES(T)REND TotalQuarteryixx^2xya+bxy/T 19972653Q12101-11121-2310499.3330.421 Q26562-981-5904576.1971.138 Q313193-749-9233653.0612.020 Q44684-525-2340729.9240.641 19983643Q13325-39-996806.7880.412 Q298861-988883.6521.118 Q31738711 960.5151.809 Q458583917551037.3790.564 19994769Q1461952523051114.2420.414 Q212221074985541191.1061.026 Q3227211981204481267.9701.792 Q4814121112189541344.8330.605 Total121106557221983922.083 a b38.432

18 Step 6: Find average deviation and adjust to ∑4 SALES(T)REND TotalQuarteryObsxx^2xya+bxy/T 19972653Q12101-11121-2310499.3330.421 Q26562-981-5904576.1971.138 Q313193-749-9233653.0612.020 Q44684-525-2340729.9240.641 19983643Q13325-39-996806.7880.412 Q298861-988883.6521.118 Q31738711 960.5151.809 Q458583917551037.3790.564 19994769Q1461952523051114.2420.414 Q212221074985541191.1061.026 Q3227211981204481267.9701.792 Q4814121112189541344.8330.605 Total121106557221983922.083 AdjustedAverage Q to ∑4Deviation 0.4170.415 1.0981.094 1.8801.874 0.6050.603 Total4.0003.987 Averages across quarters: Rescale to the base of 4:

19 Step 7 to 10: Set future values of x and estimate y-hat SALES(T)REND TotalQuarteryObsxx^2xya+bxy/T 19972653Q12101-11121-2310499.3330.421 Q26562-981-5904576.1971.138 Q313193-749-9233653.0612.020 Q44684-525-2340729.9240.641 19983643Q13325-39-996806.7880.412 Q298861-988883.6521.118 Q31738711 960.5151.809 Q458583917551037.3790.564 19994769Q1461952523051114.2420.414 Q212221074985541191.1061.026 Q3227211981204481267.9701.792 Q4814121112189541344.8330.605 Total121106557221983922.083 (T)RENDAdjustedAverage Q yxa+bxto ∑4Deviation 20006199.798Q1592.374131421.6970.4170.415 Q21645.213151498.5611.0981.094 Q32961.771171575.4241.8801.874 Q41000.440191652.2880.6050.603 Total4.0003.987 a922.083 b38.432 Trend for 2000: Estimate for y:

20 Chart Forecast

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