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Time Series. Internal AS credits. Applications : . The usage of time series models is twofold: Obtain an understanding of the underlying forces and structure that produced the observed data Forecasting , monitoring or even feedback and feed-forward control. .

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## Time Series

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**Time Series**Internal AS credits**Applications:**The usage of time series models is twofold: Obtain an understanding of the underlying forces and structure that produced the observed data Forecasting, monitoring or even feedback and feed-forward control.**Time Series Analysis is used for many applications such as:**Economic Forecasting Sales Forecasting Budgetary Analysis Stock Market Analysis Yield Projections Process and Quality Control Inventory Studies Workload Projections Utility Studies Census Analysis and many, many more...**Time Series**A time series results when an ordered sequence of values of a variable is recorded at equally spaced time intervals over a period of time.**The Four Components**We decompose a time series to highlight - trend- seasonal variation - irregular variation - cyclical variation**Trend**The Trend component is the long termpattern of change. (shown by the movement of the moving means). The trend of a set of data is modelled by a Trend Line drawn through the data plotted on a graph over time. A negative or downward trend line means contraction, a positive or upward trend line means growth.**WHAT ARE SEASONAL EFFECTS?**A seasonal effect is a systematic and calendar related effect. Some examples include the sharp escalation in most Retail series which occurs around December in response to the Christmas period, or an increase in water consumption in summer due to warmer weather. Other seasonal effects include trading dayeffects (the number of working or trading days in a given month differs from year to year which will impact upon the level of activity in that month) and moving holidays (the timing of holidays such as Easter varies, so the effects of the holiday will be experienced in different periods each year).**WHAT IS SEASONAL ADJUSTMENT AND WHY DO WE NEED IT?**Seasonal adjustment is the process of estimating and then removing from a time series influences that are systematic and calendar related. Observed data needs to be seasonally adjusted as seasonal effects can conceal both the true underlying movement in the series, as well as certain non-seasonal characteristics which may be of interest to analysts.**WHAT IS SEASONALITY?**The seasonal component consists of effects that are reasonably stable with respect to timing, direction and magnitude. It arises from systematic, calendar related influences such as: Natural Conditions weather fluctuations that are representative of the season (uncharacteristic weather patterns such as snow in summer would be considered irregular influences) Business and Administrative procedures start and end of the school term Social and Cultural behaviour Christmas**HOW DO WE IDENTIFY SEASONALITY?**Seasonality in a time series can be identified by regularly spaced peaks and troughs which have a consistent direction and approximately the same magnitude every year, relative to the trend.**Figure 1: Monthly Retail Sales in New South Wales (NSW)**Retail Department Stores**The irregular component (sometimes also known as the**residual) is what remains after the seasonal and trend components of a time series have been estimated and removed. It results from short term fluctuations in the series which are neither systematic nor predictable. In a highly irregular series, these fluctuations can dominate movements, which will mask the trend and seasonality. The following graph is of a highly irregular time series WHAT IS AN IRREGULAR COMPONENT?**Figure 2: Monthly Value of Building Approvals, Australian**Capital Territory (ACT)**The cyclical component is the periodic contraction and**expansion that occurs over a period of time, of more than one year. This component is usually ignored when short term forecasts are derived. E.g. the business cycles showing periods of prosperity and depression. The business cycle is probably caused by the effect of rises and falls in business optimism or stock levels CYCLICAL VARIATION**By extending beyond the range of the historical data**(extrapolation) we can forecast future data values: sales, commodity prices etc. Note: Extreme care must be used when extrapolating data, since there is no guarantee that the historical trend will continue unchanged into the future. Forecasts**Figure 1: Monthly Retail Sales in New South Wales (NSW)**Retail Department Stores**Features of Time Series**• Long Term Trend (also called general trend or secular trend) • Periodic Movements • Seasonal variation: oscillations due to changes in seasons • Cyclic Movements: oscillations due to longer term influences such as cyclic weather patterns or economic patterns (time period larger than 1 year) • Random or Irregular movements • Spikes or troughs • A ramp is a step up or step down and then the periodic movements continue as normal after the ramp.**Two Content Layout with Table**• First bullet point here • Second bullet point here • Third bullet point here**Two Content Layout with SmartArt**• First bullet point here • Second bullet point here • Third bullet point here

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