2. Minister of Finance

3. Instructor: Le Thi Ngoc Tu Group members: Tran Tien Manh Pham Thi Huyen Ly Thi Thuy Linh Nguyen Van Hiep

4. Introduction Overview Components of time series Analysis Smoothing techniques Trend analysis Measuring seasonal effect Forecasting Time-series forecasting with regression Application 3

5.  Recall Regression Model X: independent variable Y: dependent variable  Time-series: - Definition: Variable measured over time in sequential order - Independent variable: Time 4

6. Example: 5

7. Purpose of time- series analysis Detect patterns to forecast the future value of the time-series Applications in management and economics Forecast interest rates, U/E rate Predict the demand for products 6

8. Long-term trend (T) Cyclical effect (C) Seasonal effect (S) Random variation (R) 7

9. + Long-term trend: Smooth pattern with duration > 1 year 8

10. + Cyclical effect: wavelike pattern about a long-term trend, duration > 1 year, usually irregular Cycles are sequences of points above & below the trend line Time Volume 9

11. + Seasonal effect: like cycles but short repetitive periods, duration < 1 year (days, weeks, months…) Sales peak in Dec. 10

12. + Random variation: irregular changes that we want to remove to detect other components Time Volume Random variation that does not repeat 11

13.  Purpose: Remove random fluctuation to detect seasonal pattern  2 types: - Moving average (MA) - Exponential smoothing 12

14. Example of Moving average: Period t ytyt 3-period MA 4-period MA 4-period centred MA 112--- 21815.33-- 31619.3317.518.13 42419.0018.7518.50 51719.0018.2519.38 61619.3320.520.13 72520.6719.75- 821--- 13

15. Trend analysis Techniques Linear model: yt = β0 + β 1t + Ɛ Polinomial model Purpose Isolate the long- term trend 14

16. Calculate MAt : Mulplicative model: yt = Tt x Ct x St x Rt MAt = Tt x Ct Yt T t x Ct x S t x Rt MAt Tt x Ct Calculate average of St x Rt  St St is adjusted  SIt, so that average SI t= 1 Measuring seasonal effect = Values of St x Rt Quarter Year1234Total 2005--1.02391.0254 20060.99180.95721.02811.0318 20070.98690.95481.03161.0212 20081.00120.95921.01341.0481 20090.99000.9304-- Average (Si)0.99250.95041.02421.03163.9987 Seasonal Index (Si)0.99280.95071.02461.03194.0000

17.  Forecast of trend & seasonality: F t = [ β 0 + β 1 t ] SI t where: F t = forecast for period t SI t = seasonal index for period t 16

18. Using the following data about CPI of Viet Nam from 2005 to 2008 for forecasting CPI in 2010: 17

19. 18

20.  Reasons: - CPI is measured over time (monthly) - 3 components exist  Technique: Time-series forecasting with regression 19

21. Random variation in 2008 CPI peaks in Feb 20

22.  Trend analysis Using Excel, the trend line is: y t = 100.551 + 0.016 t y = 100.551 + 0.016 t 21

23. Calculate MAt : Mulplicative model: yt = Tt x Ct x St x Rt MAt = Tt x Ct Yt T t x Ct x S t x Rt MAt Tt x Ct Calculate average of St x Rt  St St is adjusted  SIt, so that average SI t= 1 Measuring seasonal effect = 22

24.  Seasonal index  Apply the formula: F t = [ β 0 + β 1 t ] SI t Month123456 SI t1.00551.0170.9970.99981.00551.0005 Month789101112 SI t0.9975 0.99450.99280.99350.9988 23

25.  Forecast CPI in 2008 Forecast CPI of 2008 did not match actual CPI due to unexpected events (recession) 24

26.  Forecast CPI in 2010 25

27. - Long term trend: slight increase in CPI - Seasonal effect: peak in Feb. y = 100.551 + 0.016 t Forecasted CPI 26

28.  ‘Time Series Analysis’, Citing or referencing electronic sources of information, viewed 15 May 2010, http://www.statsoft.com/textbook/time-series- analysis/?button=3http://www.statsoft.com/textbook/time-series- analysis/?button=3  Australian Bureau of Statistics, ‘Time Series Analysis: The Basics’, viewed 15 May 2010, http://www.abs.gov.au/websitedbs/d3310114.nsf/4a256353001af3ed4 b2562bb00121564/b81ecff00cd36415ca256ce10017de2f!OpenDocume nt#WHAT%20IS%20A%20TIME%20SERIES%3F http://www.abs.gov.au/websitedbs/d3310114.nsf/4a256353001af3ed4 b2562bb00121564/b81ecff00cd36415ca256ce10017de2f!OpenDocume nt#WHAT%20IS%20A%20TIME%20SERIES%3F  ‘Introduction to Time Series Analysis’, Citing or referencing electronic sources of information, viewed 15 May 2010, http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm  Berenson, M. & Levine, D. 1998, Business Statistics - A first course, Prentice Hall Press.  Anderson, D., Sweeney, D. & Williams, T. 1999, Statistics for business and economics, South-Western College Publishing, Ohio.  Selvanathan, A., Selvanathan, S., Keller, G. & Warrack, B. 2004, Australian business statistics, Nelson Australia Pty Limited. 27

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