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 ( ) + + =