Question
If a time series exhibits a cyclical pattern that does
not follow a fixed period (e.g., economic cycles), which of the following decomposition methods would be most appropriate?Solution
STL (Seasonal-Trend decomposition using LOESS) is a robust method for decomposing time series data, particularly when the seasonality is not fixed or follows irregular cycles, such as economic cycles. Unlike traditional methods like classical decomposition, which assume a fixed seasonal period, STL uses locally weighted regression (LOESS) to estimate the seasonal and trend components, making it flexible and capable of handling non-constant seasonal patterns. STL can handle both long-term trends and irregular, cyclical components, making it an ideal choice for data with variable seasonality or unpredictable cycles. Why Other Options Are Incorrect: тАв A: Classical decomposition assumes fixed seasonality and may not be effective for cyclical patterns that do not follow a regular period. тАв B: X-11 decomposition is a variation of classical decomposition and is also designed for regular seasonality, making it unsuitable for irregular cycles. тАв D: While Seasonal-Trend decomposition using LOESS (STL) is robust, it is the best option for irregular seasonality, making this method the most appropriate. тАв E: ARIMA decomposition is designed for models involving autoregressive, differencing, and moving averages but does not explicitly handle irregular seasonal or cyclical patterns.
рдЬрд┐рди рд╕рдорд╕реНрдд рдкрджреЛрдВ рдХреЗ рджреЛрдиреЛрдВ рдкрдж рдкреНрд░рдзрд╛рди рд╣реЛрддреЗ рд╣реИрдВ , рдЙрдиреНрд╣реЗрдВ рд╣реИрдВя┐╜...
рднреВрдорд┐рдЬрд╛ , рд╡реИрджреЗрд╣реА, рд░рд╛рдордкреНрд░рд┐рдпрд╛ рдХрд┐рд╕рдХреЗ рдкрд░реНрдпрд╛рдп рд╣реИрдВ?
тАЬрдЖрдк рдбреВрдмреЗ рддреЛ рдЬрдЧ рдбреВрдмрд╛ рдХрд╛ рдЕрд░реНрде рд╣реИтАЭ рдореБрд╣рд╛рд╡рд░реЗ рдХрд╛ рдЕрд░реНрде рд╣реИ?
рд╣рд┐рдВрджреА ( 1) рджреЗрд╡рдирд╛рдЧрд░реА ( 2) рд▓рд┐рдкрд┐ рдореЗрдВ ( 3) рдЬрд╛рддреА ( 4) рд╣реИ ( 5) рд▓рд┐рдЦреА ( 6) ред
рд╣рд┐рдиреНрджреА рд╡рд░реНрдгрдорд╛рд▓рд╛ рдореЗрдВ рдКрд╖реНрдо рд╡реНрдпрдВрдЬрди рдХреМрди рдХреМрди рд╕реЗ рд╣рд╛рддреЗ рд╣реИрдВ?
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдореЗрдВ рд╕реЗ рдХреМрди рд╕рд╛ рд╢рдмреНрдж рддрддреНрд╕рдо рдирд╣реАрдВ рд╣реИ?
'рдкрдЯреНрдЯреА рдкрдврд╝рд╛рдирд╛' рдореБрд╣рд╛рд╡рд░реЗ рдХрд╛ рдЕрд░реНрде рд╣реИ
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдореЗрдВ рдХрд┐рд╕рдХреА рд╡рд░реНрддрдиреА рд╢реБрджреНрдз рд╣реИ- ?
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдореЗрдВ рд╕реЗ рдХреМрди-рд╕рд╛ рд╢рдмреНрдж ' рдкрддрд┐ ' рдХрд╛ рдкрд░реНрдпрд╛рдпрд╡рд╛рдЪреА рд╣реИ ?
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдореЗрдВ рдХреМрди рд╕рд╛ рд╡рд╛рдХреНрдп рд╢реБрджреНрдз рд╣реИ ?