CHAPTER 1: An introduction to time series and forecasting

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35 Temperature in Hong Kong (1994-1997) daily temperature in HK 30 25 20 15 10 5 0 200 400 600 800 1000 1200 Number of patients with respiratory problems in Hong Kong (1994) 300 no. of patients 250 200 150 100 0 50 100 150 200 250 300 350 400 time (daily) 10000 Measles cases in London (1944-1978) cases of measles 8000 6000 4000 2000 0 0 100 200 300 400 500 600 700 800 900 1000 time (week) DOW stock index (1992-2005) 15000 DOW index 10000 5000 0 1992 1994 1996 1998 2000 2002 2004 time return: z t = log(y t ) −log(y t−1 ) 0.1 0.05 0 −0.05 −0.1 1992 1994 1996 1998 2000 2002 2004 time 4
2 Forecasting A major objective of time series analysis is forecasting of future values of the series e.g. what will be the unemployment rate next year? Is there a trend in global temperature? what is the seasonal effect? what is the relationship between GDP and interest rate? Forecasting methods: 1. Qualitative forecasting methods: use the opinions of experts to predict future events subjectively. 2. Quantitative forecasting methods: Based the historical data, use statistical methods to predict future values of a variable. 3 The difference between the time series and IID statistics Time series data are dependent 1. there is an order for the observation of time series. 2. time series data are dependent. e.g. this month’s unemployment rate will be correlated with the last month’s. The problem with dependence: Consider the IID case X 1 , X 2 , · · · , X n random sample with mean µ and variance σ 2 . Then we estimate µ by ˆµ = (X 1 + X 2 + · · · + X n )/n 5
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Page 3: Example (Unemployment Rate (%) in S

CHAPTER 1: An introduction to time series and forecasting

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