第14章时间序列分析 nalysIs
第14章 时间序列分析 Time-Series Analysis
本章概要 Component Factors of the Time-Series model Smoothing of Data Series 口 Moving averages a Exponential Smoothing Least square Trend Fitting and forecasting a Linear, Quadratic and Exponential Models Autoregressive models Choosing Appropriate models Monthly or Quarterly data
本章概要 • Component Factors of the Time-Series Model • Smoothing of Data Series Moving Averages Exponential Smoothing • Least Square Trend Fitting and Forecasting Linear, Quadratic and Exponential Models • Autoregressive Models • Choosing Appropriate Models • Monthly or Quarterly Data
What Is Time-series A Quantitative Forecasting Method to Predict Future values Numerical Data Obtained at regular Time Intervals Projections Based on Past and Present Observations Example: Year:19941995199619971998 aes 75.374.278.579780.2
What Is Time-Series • A Quantitative Forecasting Method to Predict Future Values • Numerical Data Obtained at Regular Time Intervals • Projections Based on Past and Present Observations • Example: Year:1994 1995 1996 1997 1998 Sales: 75.3 74.2 78.5 79.7 80.2
Time-Series Components 时间序列的组成 Trend Cyclical Time-Series Seasonal Random
Time-Series Components 时间序列的组成 Time-Series Cyclical Random Trend Seasonal
Trend Component 趋势项 Overall Upward or Downward movement Data Taken over a period of years Sales Upward trend Time
Trend Component 趋势项 • Overall Upward or Downward Movement • Data Taken Over a Period of Years Sales Time
Cyclical component 周期项 Upward or Downward Swings May vary in Length Usually Lasts 2-10 Years Sales Cycle Time
Cyclical Component 周期项 • Upward or Downward Swings • May Vary in Length • Usually Lasts 2 - 10 Years Sales Time
Seasonal Component 季节项 Upward or Downward Swings Regular Patterns Observed within 1 Year Sales Inter Time Monthly or Quarterly)
Seasonal Component 季节项 • Upward or Downward Swings • Regular Patterns • Observed Within 1 Year Sales Time (Monthly or Quarterly)
Random or lrregular component 随机项 Erratic, Nonsystematic, Random, th esidual? Fluctuations Due to Random variations of 口 Nature 口 Accidents Short duration and Non-repeating
Random or Irregular Component 随机项 • Erratic, Nonsystematic, Random, 慠 esidual?Fluctuations • Due to Random Variations of Nature Accidents • Short Duration and Non-repeating
Multiplicative Time-Series Model 相乘时间序列模型 .Used Primarily for Forecasting Observed Value in Time Series is the product of Components For annual data Ti=Trend Y1=T×C;×l Ci Cyclical For Quarterly or monthly Data i =Irregular Y1=71×S;×C1×l i S:= Seasonal
Multiplicative Time-Series Model 相乘时间序列模型 •Used Primarily for Forecasting •Observed Value in Time Series is the product of Components •For Annual Data: •For Quarterly or Monthly Data: i i i i Y = T C I i i i i i Y = T S C I Ti = Trend Ci = Cyclical I i = Irregular Si = Seasonal
Moving Averages 移动平均 Used for Smoothing Series of arithmetic means over time Result dependent upon choice of l, length of Period for Computing means For Annual Time-series Should be odd Example: 3-year Moving Average 口 First Average MA(3/≈y1+Y2+Y 3 口 Second Average: MA(3) 2+Y3+Y 3
Moving Averages 移动平均 • Used for Smoothing • Series of Arithmetic Means Over Time • Result Dependent Upon Choice of L, Length of Period for Computing Means • For Annual Time-Series, L Should be Odd • Example: 3-year Moving Average First Average: Second Average: 3 3 Y1 Y2 Y3 MA ( ) + + = 3 3 Y2 Y3 Y4 MA ( ) + + =