**BRIEF description**of "Analysis and time series prediction subsystem" in OpenWebGIS.

For analyzing and forecasting of time series the method of singular spectrum analysis (SSA http://en.wikipedia.org/wiki/Singular_spectrum_analysis) is used in OpenWebGIS . Using an integral part of this method in OpenWebGIS, you can obtain the singular decomposition of the matrix. The results of Singular value decomposition of matrix (SVD-decomposition http://en.wikipedia.org/wiki/Singular_value_decomposition) can be used for other tasks of mathematical analysis.

In OpenWebGIS SVD-decomposition algorithm is implemented on the basis of one variant of algorihtm close to the one realised in software library LINPACK (LAPACK) https://en.wikipedia.org/wiki/LINPACK.

The algorithm of SVD-decomposition was created by OpenWebGIS developers strictly according to the rules of numerical linear algebra with the help of Javascript programming language. In order to start the work with subsystem of analysis and time series prediction you need to select the menu item "Calculations-> Time and matrix analysis".

In many cases objects or processes and natural phenomena around us are the source of large amounts of diverse information, which can be collected and analyzed. The collected data often can be represented in the form of time series. For their effective research it is advisable to use an automated analysis, including forecasting of spatial and temporal distribution of various objects and settings.

To analyze the dynamics of the time series and forecasting spatial-temporal distribution of objects in OpenWebGIS a powerful and fast-paced method of singular spectrum analysis is used.

This method has some advantages in the prediction of irregular, non-stationary time series, taking place in the statistical observations of the real technogenic or natural objects. OpenWebGIS provides visual interactive way to work with this method for the analysis and prediction of time series.

The method of SSA (SSA) is used to decompose time series into additive components, which allows to solve the following tasks:

- Selection of the trend in the changes of the processes under study;

- Periodicities discovering in objects changes and their distribution;

- Smoothing of the series, excluding the random errors (noise).

In OpenWebGIS it is possible to analyze and predict the time series which have a spatial reference (coordinate) and those which do not have such binding (in this case, simply add the data columns coordinates having, for example a zero value).

Futher in the article the usage of "Analysis and time series prediction subsystem" in OpenWebGIS is shown in the example of work with the following data of sea surface temperature in the region bounded by the following coordinates: Longitude 10W to 20W, Latitude 30N to 36N are shown in the attached screenshots. The data is limited in time Jan 2000 to Aug 2013. The temperature data in CSV format are taken from here: http://iridl.ldeo.columbia.edu/SOURCES/.IGOSS/.nmc/.Reyn_SmithOIv2/.monthly/.sst/T/463.5/643.5/RANGE/ngridtable/dataselection.html?limit.X.value=10W+to+20W&limit.Y.value=30N+to+36N&limit.T.value=Jan+2000+to+Aug+2013

At first add the data you want to analyze on the map in the form of a vector layer data. To do this, select the appropriate menu item "Layers-> New Layer from ..." as shown in

**Figure**

**1**.

**Figure 1**.

Next the screenshots show the outdated OpenWebGIS interface, but since there were only small changes in the interface, these screenshots will be a good help for you to understand how to work with "Analysis and time series prediction subsystem" in OpenWebGIS.

In order to start the work with subsystem of analysis and time series prediction you need to select the menu item "Calculations-> Time and matrix analysis" (See

**Figure 2**).

**Figure 2.**

Then, in the appeared pop-up window (see Figure 3), enter the window length in accordance with the recommendations of the method of SSA

(see the book by Golyandina N., Nekrutkin V., and Zhigljavsky A. "Analysis of Time Series Structure: SSA and Related Techniques". London: Chapman & Hall/CRC, 2001. 305 p, here some information is presented from these authers: http://www.gistatgroup.com/cat/examples/ssa_for_en.pdf). The choice of "window length"

**L**in performing the SSA decomposition must depend on the properties of the time series and the purpose of the analysis. For example "window length"

**L**can be multiple of seasonal component. The most detailed decomposition is achieved when the window length is approximately equal to half of time series length, that is when

**L**∼ N/2, where N is length of time series.

Layer, containing the temperature data, is in our case called “datafile2000_2013”. Before the start of the analysis it should be selected in the list of

__as shown in__

**"Editable Layer"****Figure 3**. If in the layer the data are aggregated by squares (spatial squares), then SSA in OpenWebGIS can be executed both in each square separately, and in all the squares immediately in automatic mode. In the case of performing the analysis in each square separately, the users can choose which time series component (trend, part of the trend, harmonics, or any of its parts) they will analyze, predict and create charts.

**Figure 3**.

After selecting the window length and the square for analysis (if you set a tick in the checkbox "Use aggregated Layer") and pressing the "OK" button for the user the windows will open with the results of SVD-decomposition in the matrix form and the form of charts of Eigen function and Principal Components. The result of analyzing the temperature data (described above) is shown in

**Figure 4,5**.

**Figure 4**.

**Figure 5**.

After done SVD-decomposition, users can specify which principal components (

**PC1, PC2, PC3 ...**) belong to the trend or harmonic, create the charts and forecasts for any time duration (number of steps). All of these options are shown in

**Figure 6**, and they appear only after the SVD-decomposition.

**Figure 6**.

If the user has correctly pointed out all of the options in the window shown in Figure 6, then after pressing the "Forecast series" button OpenWebGIS will create the chart on the background of the real data (See

**Figure 7**).

**Figure 7**.

If the forecast is done automatically for all spatial squares of the aggregated layer at once, then the geographical layer will be created containing the predicted values (in this case the temperatures in the squares of 2x2 degrees). The comparison of calculated prediction values and real temperatures occured in selected temporal and spatial interval is shown in

**Figure 8**. As it can be seen from the figure SSA method in the most of squares has given a good prediction of temperature on the ocean surface. This method allows to analize and predict any other numeric parameters of real objects.

**Figure 8**.