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I am trying to estimate garch parameters for returns of an index. The index returns are for period of 1 year. The garch parameters are estimated for 2 seperate periods both having 1 year data. Parameters computed by eviews are as under-

Period 1
Omega: 0.000113768
Alpha: 0.023693849
Beta: 0.921176835

In the next period the parameters computed by eviews were very different

Period 2
Omega: 0.00003841152
Alpha: -0.047642246
Beta: 1.024134843

Apparently the parameters estimated do not appear to be correct for the Period 2. Is there any setting to be done in eviews before estimation? Is the period of 1 year too short for estimation of garch parameters? Please let me know.

Can anyone suggest how to set non negative condition while estimation of GARCH parameters so that alpha, beta < 1 and alpha + beta+gamma = 1

The data do not display GARCH behavior. You should first check the diagnostics before moving on to the estimation.

How do i specify alpha and beta values to be less than 1 in eviews while estimation of garch parameters?

Actually, you do not. Such constraints (including the nonnegativity of estimated parameters) can be too restrictive. If your data display any GARCH-type behavior, then the parameters should be estimated within their domains. Once you make sure that the mean equation is stationary, you can then try alternative volatility models. Those constraints can be useful for ex-post checking of the stability of your model.

How to find out if the data displays garch behaviour? Is there any facility in Eviews or excel to find out.

See "Residual Diagnostics" section of Chapter 24 in the User's Guide I.