GCNU313A_Notes_Lecturer.docx - ITE3706 Foundation Mathematics II(A GCNU313A – Notes Unit Title Identify components of a time series and make forecasts

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ITE3706 Foundation Mathematics II(A) GCNU313A – Notes Unit Title Identify components of a time series and make forecasts Unit Code GCNU313A 1 Time Series 時間序列 Components 組成份子 A time series 時間序列 is a collection of data recorded over a period of time – usually weekly, monthly, quarterly, or yearly. An analysis of past history – time series – can be used by management to make current decisions and for long-term forecasting and planning. Typically such time series data exhibit one or more of the following components. 1. Trend T 長期趨勢 The trend T , also known as the long-term trend, is the smooth long-term trend of the data. Long-term trends of sales, employment, stock prices, and other business and economic series follow various patterns. Some move steadily upward, others decline 下跌 , and others stay the same over a period of time. Upward Downward Remained relatively constant The following figure shows the Hang Seng Index from Dec, 1986 to Jan, 2012. p. 1 of 15
ITE3706 Foundation Mathematics II(A) GCNU313A – Notes 2. Seasonal 季節的 Variation S 變動 The seasonal variation S , describes the fluctuations 波動 in the time series that recur 循環 during specific time periods. The unit of time may be quarterly, monthly, weekly, or even daily. For example, an ice-cream manufacturer may regularly experience peaks 高峰期 for sales in summer months and troughs 低谷期 for sales in winter months. A short-term pattern repeats yearly. In the below figure, a clear upward trend is evident, around which there is seasonal variation, with quarter 2 representing successive peaks and quarter 4 successive troughs within each year. 3. Cyclical 循環的 Variation C 變動 The cyclical variation C , generally describes fluctuations of the time series about the trend that are attributable to business and economic conditions. A typical business cycle consists of a period of prosperity followed by periods of recession 衰退 , depression 蕭條 , and recovery 復元 . There are sizable fluctuations, representing more than one year in time, above and below the trend. In the below figure, a clear upward trend is evident, around which there is cyclical variation with a period of around ten years between successive peaks and successive troughs. p. 2 of 15 Source: HK Hang Seng Indexes Source: Hang Seng Indexes Source: Hang Seng Indexes
ITE3706 Foundation Mathematics II(A) GCNU313A – Notes 4. Irregular 不規律的 Variation I 變動 Many analysts prefer to subdivide the irregular variation I into episodic 插曲式的 and residual 剩餘的 variations. Episodic fluctuations are unpredictable, but they can be identified. The initial impact on the economy of a war can be identified, but it cannot be predicted. After the episodic fluctuations have been removed, the remaining variation is called the residual variation. The residual fluctuations, often called chance fluctuations, are unpredictable, and they cannot be identified. The presence of the

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