Minister of Finance

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

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

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

Example: 5

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

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

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

+ 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

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

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

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

Example of Moving average: Period t ytyt 3-period MA 4-period MA 4-period centred MA

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

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 Average (Si) Seasonal Index (Si)

 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

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

18

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

Random variation in 2008 CPI peaks in Feb 20

 Trend analysis Using Excel, the trend line is: y t = t y = t 21

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

 Seasonal index  Apply the formula: F t = [ β 0 + β 1 t ] SI t Month SI t Month SI t

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

 Forecast CPI in

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

 ‘Time Series Analysis’, Citing or referencing electronic sources of information, viewed 15 May 2010, analysis/?button=3http:// analysis/?button=3  Australian Bureau of Statistics, ‘Time Series Analysis: The Basics’, viewed 15 May 2010, b2562bb /b81ecff00cd36415ca256ce10017de2f!OpenDocume nt#WHAT%20IS%20A%20TIME%20SERIES%3F b2562bb /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,  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

28