In ArcGIS as extent of your interpolation the extent of your input point feature is used. If you want to use another extent, you can set it in the Environment settings of your tool.

But careful: outside the extent of your points you will not interpolate but extrapolate, which usually make no sense!

Thus the problem is, that your data is not covering your whole study area

Just as Dietrich pointed out, you want to extrapolate to the areas with no data but be careful. However, this step may help you.

Interpolation->Krigging-> Environments (at the base of the krigging window interface)-> Processing extent-> Extent -> Select your study area' shapefile ->Ok. Now, you can start your interpolation.

You have to check extent of your interpolation using the Environment setting tool of ArcMap

Hey! If You don't have more points to interpolation - try another method (i.e. Topo-To-Raster). Normally, kriging doesn't cover its range entire area, but only points. All the best!

For this method, the parameter of the extend is certainly the problem.

Otherwise the parameter of the variogram...

But in interpolation you may have a lot of method linear or no:

IDW

kriging

By natural neighbors

spline

Spline with interrupts

Topo to raster

Trend

So, you can find some information about this on the web :

I know that IDW is a linera method but this you test it ?

https://desktop.arcgis.com/fr/arcmap/latest/extensions/geostatistical-analyst/an-introduction-to-interpolation-methods.htm

http://pro.arcgis.com/fr/pro-app/tool-reference/3d-analyst/comparing-interpolation-methods.htm

Good read.

As noted by several respondents, the limitation is a feature of the software and not of the algorithm. Kriging (Simple, Ordinary, Universal) is based on several statistical assumptions and these are implicitly connected to the region of interest, i.e. when the region is enlarged the assumptions may no longer be valid. The assumptions are not connected/limited to the set of data locations. Unfortunately in most practical applications the only available information about the validity of the statistical assumptions comes from the data (sometimes from other knowledge about the phenomenon that generated the data.)

Most interpolation algorithms (kriging, radial basis functions, IDW, nearest neighbor, etc) do not explicitly distinguish between interpolation and extrapolation, there is no absolute and clearly defined boundary between the two.

You can find some papers which discuss incorporating boundary conditions with interpolation but that is a different problem.

Dear Naveed, in order to cover the whole area with kriging interpolation, the extent should be a polygone that cover all region area.

The limit of your interpolation is given by the data coverage you have, not by the project area (or polygon) itself. It is a good practice to maitain the interpolation area around your data coverage not far away despite it looks prettier to see the complete area covered. Some people define the data influence by creating a buffer around the sampling data. You can create the buffer of influence by using the distance indicated by the variogram. Best luck!

You should set the extents of any tool in the Environment tab. You will find the analysis extent option there. Just for advice, if in case you try to extrapolate beyond the input points, you might get some meaningless results.

Adjust the 'size of the interpolation area' in the setting, It can take another square by default, so you need to check up the real area of interest (mask).

Except in mining applications ; treatment of stationarity and the introduction of intrinsic stationarity; introduction of semi-variogram for

the study of spatial relations; interpolation of data by the kriging method. .Variographic analysis can be used in mixed models, for

analyze the residues.

Geostatistics owes its name to the mining origins of the discipline (Krige, Matheron). Many of the fundamental concepts of the discipline come from the work of Georges Matheron (variable regionalised, random function, intrinsic hypothesis, nugget effect 1, MATHERON et al. 1965). Figure 5.1 presents a summary illustrating the journey of reality towards a more abstract model, model that will allow itself to act in a way that we hope optimal (CHAUVET 2008).