The analytical process of the time series analysis method includes

Time series data analysis steps

Time series data analysis steps are as follows:

1, with observation, survey, statistics, sampling and other methods to obtain the observed system time series dynamic data.

2, according to the dynamic data for correlation diagram, correlation analysis, autocorrelation function. The correlation diagram can show the trend and cycle of change, and can find the jump point and inflection point. A jump point is an observation that is inconsistent with other data. If the jump points are correct observations, they should be taken into account in modeling, and if they are anomalies, the jump points should be adjusted to the desired values.

3. The inflection point is the point at which the time series suddenly changes from an upward trend to a downward trend. If there is an inflection point, the time series must be modeled with a different model to fit the time series in segments, such as using a threshold regression model.

4. Identify a suitable stochastic model for curve fitting, i.e., use a generalized stochastic model to fit the observed data of the time series. For short or simple time series, trend models and seasonal models with errors can be used for fitting.

5. For smooth time series, the general ARMA model (autoregressive sliding average model) and its special case autoregressive model, sliding average model or combined-ARMA model, etc. can be used for fitting. The ARMA model is generally used when there are more than 50 observations.

6, for the non-stationary time series, the observed time series should be first differential operation, into a smooth time series, and then use the appropriate model to fit the differential series.

Overview of Time Series Analysis

Time series have the following characteristics:

Classification:

Five steps: characterization, model identification, model parameter estimation, model testing, and model application.

In the process of time series modeling, the first thing to do is to have an understanding of the characteristics of the time series, in general, from the stochasticity of the time series, smoothness and seasonality of the three aspects of the time series to be considered, of which smoothness is particularly important, for a non-smooth time series, usually need to be smoothed in the modeling after the modeling, but also according to the characteristics of the model between the model.

The unit is the unit of the time series.

The unit root test is to determine whether there is a unit root in the time series, that is, to test the smoothness of the time series. It can be proved that if there is a unit root, the sequence is not smooth, commonly used unit root test methods include: ADF (AugmentedDickeyFuller) test, PP (PhillipsPerson) test, NP (NelsonPlosser) test and so on.

The model identification of time series mainly includes: determining the model category and model order two aspects.

In terms of determining the category of time series models, the trailing and truncated nature of the autocorrelation function and partial correlation function of the smooth series samples is the basic method of determining the model category.

In terms of determining the order of the time series model, there are mainly the following ways to fix the order.

The test of the time series model is divided into two categories: the significance test of the model and the significance test of the model parameters

The significance test of the time series model is mainly to test the validity of the model. The main task of the significance test of the model is to see whether the model is fully effective in extracting all the information, that is, a good model should ensure that the residuals of the series of white noise, so as to ensure that there is no more information available. If the residuals are non-white noise, it means that relevant information is left in the residuals.

Significance testing of model parameters is to test whether each parameter in the model is significantly different from zero, with the goal of making the model more streamlined and accurate. If the model contains non-significant parameterization, it can indicate parameter redundancy on the one hand, and on the other hand, it can affect the estimation accuracy of other parameters. Therefore it is important to present those parameters in the model that are not significant.

Predictive analysis using the model.

Reference: “Time Series Modeling and Forecasting” by Lizhu Wang; Science Press

16 Common Data Analysis Methods-Time Series Analysis

Time series (timeseries) is a system in which the observed values of a certain variable are arranged into a numerical sequence according to the order of time (with the same time intervals) to demonstrate the process of change of the object of study within a certain period of time, and to find and Analyze the change characteristics, development trend and law of things. It is the total result of the influence of a variable in the system by various other factors.

The main purpose of the study of time series can be forecasting, based on the existing time series data to predict future changes. The key to time series forecasting: determining the pattern of change in an existing time series and assuming that this pattern will continue into the future.

Basic Characteristics of Time Series

It is assumed that trends in the development of things extend into the future

The data on which the forecasts are based are irregular in nature

The causal relationships between developments are not taken into account

Time-series data are used to characterize the development of phenomena over time.

Time series considerations

Time Series >

Time series analysis is divided into traditional time series analysis and modern time series analysis in terms of the historical stage of its development and the statistical analysis methods used. Depending on the time of observation, the time in a time series can be can be a year, a quarter, a month, or any other form of time.

The main considerations in time series analysis are:

long-termtrend

The time series may be fairly stable or show some trend over time.

Time series trends are generally linear, quadratic, or exponential.

l Seasonalvariation

Sequence that varies in time and exhibits repetitive behavior.

Seasonal variations are usually related to date or climate.

Seasonal variations are usually associated with annual cycles.

lCyclicalvariation

Time series may undergo “cyclical variations” as opposed to seasonal variations.

Cyclical movements are usually due to economic changes.

lRandom effects

On top of that, there are also contingent factors that affect the time series, resulting in some kind of random fluctuation in the time series. Time series to remove the trend, cyclical and seasonal fluctuations of chance, known as random (random), also known as irregular fluctuations (irregularvariations).

Major Components of Time Series

The components of a time series can be categorized into four types:

l Trend (T),

l Seasonal or Seasonal Variation (S),

l Cyclical or Cyclical Fluctuation (C),

l Random or Irregular Fluctuation (I).

One of the main elements of traditional time series analysis is to separate these components from the time series and express the relationship between them in a certain mathematical equation, and then analyze them separately.

Basic Steps of Time Series Modeling

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1) Obtain the observed system time series dynamic data by observation, survey, statistics, sampling and other methods.

2)Make a correlation diagram based on the dynamic data, perform correlation analysis, and find the autocorrelation function.

Correlation plots show trends and cycles of change and can detect jump and inflection points.

A jump point is an observation that is inconsistent with other data. If the jump point is a correct observation, it should be taken into account in modeling, and if it is an anomaly, the jump point should be adjusted to the desired value.

The inflection point, on the other hand, is the point at which the time series suddenly changes from an upward trend to a downward trend. If there is an inflection point, the time series must be modeled to fit the time series in segments using a different model, such as a threshold regression model.

3) Identify a suitable stochastic model for curve fitting, i.e., use a generalized stochastic model to fit the observed data of the time series.

For short or simple time series, trend and seasonal models with errors can be used for fitting.

For smooth time series, they can be fitted with the generalized ARMA model (autoregressive sliding average model) and its special case autoregressive model, sliding average model, or combined-ARMA model.

The ARMA model is generally used when there are more than 50 observations. For non-stationary time series, the observed time series should be first differentiated into a stationary time series, and then the appropriate model should be used to fit this differentiated series.

The first step: the definition of the date scalar:

Open the data file, click “Data”, select “Define Date and Time”, the “Define Date” dialog box pops up,

Data in the beginning of the data is the first time of the cell inside the data file, my first is August 1997, every time. The first is August 1997, each line represents the monthly sales, therefore, you need to “define the date” dialog box from the left side of the “case is” box, select “year, month”, enter ‘1997’ on the left side of the month box, enter ‘8’, said The starting month of the first case is August 1997,

Finally click on the confirmation, so that the spss data file will be generated inside the three new variables

The following figure:

. Step 2: Understand the trend of the time series

Understanding the trend of the time series to do a series of tables can be, click “Analysis”, inside the selection of “Time Series Forecasting, select” Sequence Diagram “dialog box, and then move the ‘Mean’ to the “Variable” box inside the ‘DATE_’ move to the “Variable” box inside the ‘DATE_’ move to the “Variable” box inside the ‘DATE_’ move to the “Variables” box inside the “Variables” box inside the “Variables” box inside the “Variables” box inside the ‘DATE_” box. ‘ move to the “Timeline Label” box, click “OK”. The result is shown in the figure

According to the analysis of the sequence diagram, we know that the fluctuation of the sequence with the seasonal fluctuation is getting bigger and bigger, so we choose the multiplication model;

Step 3: Analyze

The third step: analyze

Click “Analyze”, select the time series forecast, and then select “Seasonal Decomposition”, the “Seasonal Decomposition” dialog box pops up, after confirming that there is no error. Click OK, as shown:

There are four more variables:

lERR means error analysis;

lSAS means seasonally corrected series;

lSAF means seasonal factor;

lSAF means seasonal factor;

lSAF means seasonal factor. denotes seasonal factor;

lSTC denotes long-term trend and cyclic variation series.

We can make a sequence plot of the four emerging variables, the mean and DATE_. First make a sequence plot of ERR, SAS, STC and mean and DATE_ as follows:

And then make a separate time-series plot of SAT and DATE___

Step 4: Forecasting

1. Click Analyze, select Time Series Forecasting, and then select Create Traditional Model. traditional model”, then the “time series modeling” dialog box will pop up.

2. Move the Mean to the Dependent Variables box, and then determine the center of the Method, in the drop-down list, select Expert Modeler. Select the “Expert Modeler” item, click the right side of the “Conditions” button, pop-up “Time Series Modeler: Expert Modeler Conditions” dialog box.

3. In the “Model” tab of the “Time Series Modeler: Expert Modeler Conditions” dialog box, select “Model Type” in the “Model Type” box. In the “Model” tab of the “Time Series Modeler: Expert Modeler Conditions” dialog box, select the “All Models” item in the “Model Type” box, and check the “Consider Seasonal Models in the Expert Modeler” check box, and then tap the “Continue” button.

4. In the “Time Series Modeler” dialog box, switch to the “Save” tab, check the “Forecast” checkbox, click “Continue” button. check box, click “Export Model Conditions” box in the “XML file” behind the “Browse” button, and then set the exported model file and save the path, and then click the “OK” button on it.

After doing the above steps, there will be another column of predicted values above the original data. As shown:

The model for the predictions was saved earlier, and we’ll now utilize that model to predict the data.

1, click “Analyze”, select “Time Series Forecasting”, and then select “Apply Traditional Model” to bring up the “Apply Model Sequence” dialog box. “Apply Model Sequence” dialog box. The specific operation of the following chart:

The last step to switch to the “Save” interface, check the “predicted value” and then click OK.

The last step is to switch to the “Save” screen.

From the prediction of the value of the direct look can not be seen, you can put the predicted data and the original data to look at the next, but also directly to do the sequence of graphs can be.

This completes the model of a time series, the specific prediction of the data can be seen in the original data above the emergence of a new column of data.

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