1 / 45

week 6 objectives

Statistical Analysis in Business 2007. 2. Time Series Plot. A time series is a series of values of a numerical variable, recorded at equally spaced time points. Minitab command: Graph > Time Series Plot. Statistical Analysis in Business 2007. 3. Observe , i = 1, 2, ... , n,where T, S and C stand for 'trend', 'seasonal' and 'cyclic

oshin
Download Presentation

week 6 objectives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Statistical Analysis in Business 2007 1 Week 6 objectives 1. The general time series model 2. Trend, seasonal, cyclic and error components 3. Detrending and deseasonalisation using Minitab 4. Estimating a smooth cyclic pattern 5. Forecasting 6. Multiplicative and additive deseasonalisation

    2. Statistical Analysis in Business 2007 2

    3. Statistical Analysis in Business 2007 3 1. The general time series model

    4. Statistical Analysis in Business 2007 4 Terminology for seasonal effects A ‘period’ consists of a number of ‘seasons’ with the same pattern recurring in each period So the seasons could be ‘months’ within a ‘period’ of a year Or the seasons could be ‘days’ within a ‘period’ of a week Or possibly ‘quarters’ within a year, etc

    5. Statistical Analysis in Business 2007 5 Lecture exercise 1

    6. Statistical Analysis in Business 2007 6 Lecture exercise 2: quarterly data

    7. Statistical Analysis in Business 2007 7 Fitting a Time Series Model

    8. Statistical Analysis in Business 2007 8 Using Minitab to fit Time Series Models - Stage 1

    9. Statistical Analysis in Business 2007 9 Minitab output for Stage 1 Trend line Seasonal indices Boxplots of data, residuals (both indexed by season) Time series plots of original data deseasonalised data (seasonally adjusted) detrended data both detrended and deseasonalised data Which of these plots is used to estimate underlying cycles?

    10. Statistical Analysis in Business 2007 10 Lecture example 2

    11. Statistical Analysis in Business 2007 11 Stage 1: Time series plots

    12. Statistical Analysis in Business 2007 12 Stage 1: Boxplots of data and residuals

    13. Statistical Analysis in Business 2007 13

    14. Statistical Analysis in Business 2007 14 Interpreting coefficients The coefficient of slope is interpreted as in linear regression, after seasonal effects have been removed Similarly, the seasonal coefficients are interpreted as the difference of average responses for particular seasons from the overall average within a period, after trend effects have been removed To de-trend, Minitab subtracts the trend line equation from the original data series To de-seasonalise, Minitab subtracts seasonal coefficients from the original data Note: all this is for additive de-seasonalisation

    15. Statistical Analysis in Business 2007 15 Interpreting trend in ‘Building Starts’ example

    16. Statistical Analysis in Business 2007 16 Interpreting seasonal coefficients in ‘Building starts’ example

    17. Statistical Analysis in Business 2007 17 Stage 2: Methods for smoothing the residuals

    18. Statistical Analysis in Business 2007 18 Methods for smoothing the residuals

    19. Statistical Analysis in Business 2007 19 Methods for smoothing the residuals

    20. Statistical Analysis in Business 2007 20

    21. Statistical Analysis in Business 2007 21 Methods for smoothing the residuals

    22. Statistical Analysis in Business 2007 22 An example of the exponential smoothing when ? = 0.8

    23. Statistical Analysis in Business 2007 23 Moving averages: pros and cons + a simple method + the effect of having k too large (oversmoothing) or k too small (undersmoothing) is understandable - a piece of the series is lost at each end - so MA is not suitable for forecasting and prediction

    24. Statistical Analysis in Business 2007 24 Exponential smoothing: pros and cons + Better for prediction than MA - A parameter called alpha (?) needs to be chosen. This measures the relative weight given to the present observation compared to the past observations - The lower the value of alpha, the more smoothing is used - There is an in-built lag, which shifts any pattern to the right

    25. Statistical Analysis in Business 2007 25 After detrending and deseasonalising, smoothing to estimate a smooth underlying cycle Minitab command: Stat>Time Series>Moving average. Select the residuals column stored from the decomposition stage, say RESI1, as Variable, enter 8 as MA length, tick Center the moving averages, and then tick Plot smoothed vs. actual under Results.

    26. Statistical Analysis in Business 2007 26

    27. Statistical Analysis in Business 2007 27 Another smoothing example

    28. Statistical Analysis in Business 2007 28 Another smoothing example

    29. Statistical Analysis in Business 2007 29 In Time series decomposition, when residuals are smoothed to estimate underlying cyclic terms, what order of moving average should be used? A good principle is to choose a multiple of the number of seasons in a period. This eliminates any inaccuracies arising from the estimation of seasonal coefficients. For example, for quarterly data, choose from MA(4), MA(8), MA(12) etc.

    30. Statistical Analysis in Business 2007 30 Forecasting Minitab provides forecasts from Time series model fitting (tick the box Generate Forecasts in the Dialogue Box, and enter details) Forecasting into the immediate future is more reliable than the far future The immediate past needs to be representative of the near future, ie conditions need to be stable

    31. Statistical Analysis in Business 2007 31 Minitab forecasts of the next four quarters

    32. Statistical Analysis in Business 2007 32 Additive and multiplicative models

    33. Statistical Analysis in Business 2007 33 How to recognise whether additive or multiplicative deseasonalisation is needed? Additive when fluctuations from one observation to the next have the same scale throughout the time series Multiplicative when scale of the fluctuations seems proportional to the general response level

    34. Statistical Analysis in Business 2007 34 Lecture exercise 6

    35. Statistical Analysis in Business 2007 35 Lecture example 3

    36. Statistical Analysis in Business 2007 36 Lecture example 3 continued

    37. Statistical Analysis in Business 2007 37

    38. Statistical Analysis in Business 2007 38 Interpretation of multiplicative seasonal indices for the jeans example

    39. Statistical Analysis in Business 2007 39 Lecture exercise 8 If trend effects are removed, for what proportion of months are the monthly sales more than 10% different from the annual average?

    40. Statistical Analysis in Business 2007 40 Estimated cycles from smoothed residuals for the jeans example

    41. Statistical Analysis in Business 2007 41 Review of fitting a Time Series Model

    42. Statistical Analysis in Business 2007 42 ‘Building starts’ example – Steps 1 & 2

    43. Statistical Analysis in Business 2007 43 Step 3 Time series decompositionStage 1: detrending and deseasonalisation

    44. Statistical Analysis in Business 2007 44 Seasonal coefficients and trend line equation

    45. Statistical Analysis in Business 2007 45 (after detrending and deseasonalising)

More Related