tag:blogger.com,1999:blog-7958828565254404797.post3749966077903675288..comments2018-02-18T11:37:28.479-08:00Comments on ListenData: Time Series Forecasting - ARIMA [Part 1]Deepanshu Bhallanoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7958828565254404797.post-64350421490005554822017-06-11T05:57:15.707-07:002017-06-11T05:57:15.707-07:00Hi Rishabh,
I believe that for white noise, at an...Hi Rishabh,<br /><br />I believe that for white noise, at any instant the probability associated with the occurence of any particular value is 0. Further, each value is indepedent of the others. These justify the fact that overall, the mean value of white noise is zero and therefore a constant.<br /><br />For a mathematical explanation,the definition of a white series is that the covariance matrix should be an identity matrix(I).<br /><br />Let x be a random vector. Covariance matrix of a random vector is E{x*x'}. Mean of the random vector is m = E{x}. Let y be a white random<br />vector with zero mean so that x = y + m.<br /><br />Now,<br />E{x*x'} = E{(y+m)*(y'+m')} = E{y*y'}+E{y*m'}+E{m*y'}+E{m*m'} = I + E{y}*m' + m*E{y'} + m*m' = I + m*m'.<br />Clearly, for x to be white series,<br />(I + m*m') should be equal to I => random vector is not white if the mean is not zero.<br /><br />Hope this helps :)Arkonoreply@blogger.comtag:blogger.com,1999:blog-7958828565254404797.post-38791847791207599372015-12-02T01:57:26.878-08:002015-12-02T01:57:26.878-08:00I am not able to understand that how it can be sta...I am not able to understand that how it can be stationary if it has sudden jumps or erratic changesRishabh Khannahttps://www.blogger.com/profile/14375879047752487288noreply@blogger.comtag:blogger.com,1999:blog-7958828565254404797.post-81210358753892260362015-12-01T12:09:48.933-08:002015-12-01T12:09:48.933-08:00A white noise series has a constant mean (of zero)...A white noise series has a constant mean (of zero), a constant variance and no correlation. Hence, it is stationary. Whereas, random walk is non-stationary as its mean and variance increases over time.Deepanshu Bhallahttps://www.blogger.com/profile/09802839558125192674noreply@blogger.comtag:blogger.com,1999:blog-7958828565254404797.post-80176544681488701712015-12-01T05:58:27.729-08:002015-12-01T05:58:27.729-08:00HI Folk,
thanks for providing us a rich article on...HI Folk,<br />thanks for providing us a rich article on Forecasting,<br />Could you please elaborate or explain White Noise again,<br />Definition above for White Noise is ONE WITH CONSTANT MEAN AND VARIATION, by this I am getting it that both mean and variance are constant.<br /><br />But when again in short definition for White noise has been explained in Random Walk column then things are quite different . It is mentioned that with zero mean and variance one.<br /><br />Could you be so kind to explain the thin line of difference between them. Rishabh Khannahttps://www.blogger.com/profile/14375879047752487288noreply@blogger.com