A time series is a list of data points in time order and is usually represented in sequence mode. Each data point can be associated with a time stamp, but it’s not required. Without special statement, the time series is taken with equally spaced time sequentially. Time series are common data, which can come from many industries, such as econometrics, finance, weather forecasting, environmental monitoring, clinical detection, control engineering, astronomy, and communications engineering.[1] Time series are largely used in business and finance that involves temporal measurements.
Examples of time series are the temperatures observed daily in a certain meteorological observatory, the counts of sunspot yearly, and the daily closing value of the Dow Jones index. Time series is also frequently visualized in line charts, where it shows the trend or seasonality in time series if it exists. The following line chart shows that there is a year by year increasing trend for the passengers by air travel, and there is a cyclical fluctuation with a peak in every July and August.
But more often, the patterns among time series data points aren’t easy to see in charts. You can use analytic methods to extract meaningful statistical characteristics from data and apply the information to predict future values. Because of the nature of temporal ordering in time series data, common statistical and data mining methods of cross-sectional data[2] aren’t suitable in these cases. So, a group of analysis methods were developed to make assumptions based on the data, where the value of the next few time points can be derived in some way from past values.
The time series analysis method can be classified in the following categories:
- Description
- Exploration
- Prediction
- Control
Note that these categories are usually overlapped by different methods. For example, forecasting is usually based on the extracted statistical model, which should be a description of time series data. The following sections provide a list of SPSS Time Series analysis methods, corresponding use cases, and access to hands-on examples. You can use the examples as a starting place for building your analysis process.
Time Series Exploration (TSE) can be the initial entry point when you begin analyzing your time series data. It is designed to analyze the characteristics of time series data with basic statistics and tests, and give some insights before modeling, such as trend, seasonality, and irregular detection. It also can be applied in the context of large-scale time series, and its time series clustering can help to understand the representative series in hundreds or thousands time series. To learn more about TSE and how to use it, see "Using IBM SPSS TSE Algorithms to Analyze Australian Wool Prices".
Exponential Smoothing (ES) methods were first used in the middle of the 20thcentury. It comes from the idea of smoothing the time series data by using a window function. In a simple moving average, the past observations are weighted equally. Exponential functions are used to assign exponentially decreasing weights as you go back in time. In ES methods, a time series is composed of three components: level, trend, and seasonality. It is an applied method for making some determination based on prior assumptions, such as a trend or seasonality in a series. To learn more about ES and how to use it, see “An Efficient Method for Time Series Forecasting—Exponential Smoothing”.
To better understand your time series data or to predict future points, there is a classical method with solid theoretical basis to help in modeling the variations in your data. It is Autoregressive Integrated Moving Average (ARIMA). The SPSS ARIMA method not only parameterizes your focused time series itself, but it can also identify whether any other provided time series contributes to the focused one, such as the pressure and humidity affecting the daily temperature, and each of the three are time series. Another example is the number of catalogs that are mailed and the number of phone lines open for ordering that impact the monthly sales of men’s clothing in a catalog company. To learn more about ARIMA and how to use it, see "Forecast Monthly Sales of Men’s Clothing with the IBM SPSS ARIMA Model".
Sometimes, the variance of a time series can be changed over time. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model describes such data with better explanation on its volatility. For example, investors often find in the financial markets that the variance of a trading price series becomes large during periods of financial crisis, but small during periods of relative steady economic growth. Specifically, the GARCH method captures the pattern of variance by a function of the past variances and the past of residuals from a mean process, then uses the function to forecast the variance in future. To learn more about GARCH and how to use it, see “Characterizing and Modeling a Time-varying Volatility Time Series with the GARCH Model”.
For the analytics scenarios with a large collection of time series and there might be causal relationships among them, Temporal Causal Modeling (TCM) can be used to discover the key temporal relationships. A relationship between a target series can be represented as deriving from the lags of several predictor series, and the target series can also become the predictors for some others. Business decision makers with TCM would know which kPIs have the important impact on the business performance and what will happen under the complex relationship. To learn more about TCM and how to use it, see “KPI Analysis Using IBM SPSS Temporal Causal Modeling”.
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Reference:
[1] Time series. In Wikipedia, The Free Encyclopedia. March 4, 2019.
[2] Cross-sectional data. In Wikipedia, The Free Encyclopedia. March 4, 2019.
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