Please see "user:3382 transfer function" for some of my reflections/advice on how to test the impact of a time series on another time series. Care should be taken to "identify/allow&...

I took your 61 consecutive days of data (24 hourly readings per day): The 1464 values were not analyzed in one model because there were essentially 24 sets of 61 historical values piggy-backed ...

When you identify an ARIMA model you should be simultaneously identifying Pulses/Level Shifts/Seasonal Pulses and/or Local Time Trends. You can get some reading material on Intervention Detection ...

If you assume a model form that is non-linear but can be transformed to a linear model such as $\log Y = \beta_0 + \beta_1t$ then one would be justified in taking logarithms of $Y$ to meet the ...

Let the data speak to the issue of which approach is more correct for any individual time series. This is what I have early championed which was ultimately and independently supported by Makridakis ...

when you have a useful model the residuals should have constant variance i.e. not dependent on level and not autoregressive in nature. Thus the residuals need to have homogenous error variance. If the ...

Whenever possible, it is best to develop one equation that effectively characterizes the data see “Joint estimation of all parameters is preferred.” from lecture 3 http://faculty.chicagobooth.edu/ruey....

Your equation is $$[y(t)-6.8840][1-.9916B]= +ϵ(t)$$ or $$y(t)= .0084\times6.8840 + .9916\cdot y(t-1)$$ $$y(t)= .0578 + .9916\cdot y(t-1)$$ What has you confused is for your stationary model the ...

Took your 2193 daily values and introduced them to AUTOBOX which detected both a significant persistent day-of-the-week pattern :day 1 & day2 (Saturday & Sunday) ... both negative and a ...

Thanks for the question as it leads to a teaching moment .... An often overlooked caveat when dealing with data is the assumption that the parameters to be optimized are invariant . In practice with ...

You can just use the history of Y or also your suggested causal. I have not seen “sample of sales” before as a causal, so I am hesitant to want to use that variable, but I am sure you know what you ...

If $$Y(t) = [\theta/\phi][A(t)+\text{IO}(t)]$$ then $$Y^\text{*}(t) = [\theta/\phi][A(t)] + [\theta/\phi][\text{IO}(t)].$$ If $$\theta = 1\ \ \text{and}\ \ \phi = [1-.5B]$$ for example ... then Y^\...

Your data set / design matrix tells a lot about your assumptions. You are explicitly assuming that week days have a common effect and weekends have a common effect. It is much more general to estimate ...

ROUND TWO: You asked “how do I do this with the log-link function and quasi(Poisson) errors?”. I say put aside your priors suggesting a particular fixed model and use a data-driven empirical process ...

Your problem arises from an over-specification. A simple first difference model with an AR(1) is quite sufficient. No MA structure or power transform is required. You could also simply model this as a ...

Your data: If you know a priori what the form of the equation is then as others have pointed out it is trivial to estimate parameters. A more general solution is to characterize the data with an ...

This problem arises quite naturally with predicting beer sales where the beer is only sold say for 5 months of the calendar year... e.g. August, September, October, November and December. Nominally ...

If the variance of the model errors is proportional to the expected value the power transforms may be appropriate When (and why) should you take the log of a distribution (of numbers)? ... your data ...

I have examined your 2 data sets ... DAILY and WEEKLY and found that your model specification for DAILY is WAYOVERCOMPLICATED while your automatic arima approach was inadequate/deficient. Both data ...

after receiving the data from the dropbox , I have some interesting things to report using AUTOBOX , a time series analusis package that I have helped to develop. To some it would appear that ...

If the variance of the errors is proportional to the expected value then a logarithmic transform transform is appropriate. Other possible relationships between the first and the second moment would ...

Standard arima software requires that the drift parameter MUST be included if there is no differencing incorporated otherwise it is optional. I have seen and used software where drift is ALWAYS an ...

your lambda value is nearly 0. , Why are you transforming the observed series ...all the assumptions are about the error series from a model. When (and why) should you take the log of a distribution (...

Sometimes too much of a good thing is not so good !. Your 1201 monthly values starting at at 1920/1 is such an example. The historical plot is hysterical suggesting that one might start with the ...

you don't want to simply introduce 1 series into the regression model with values [1,2,3,4,5,6,7,1,2,3.....] which assumes linearity between days ' BUT rather introduce 6 dummy 0/1 indicators ...

You asked 'I am looking for some resources with example problems with Time Series modelling and predictions" I answer .. look no fUrther that SE... don't limit your scholarly pursuit to a language ...

Data can have monthly effects , week within a month effects besides the effects of environmental changes. Post one of your data sets for a particular location and time available I will try to help ...

This is probably due to untreated deterministic (NOT STOCHASTIC) effects like level shifts or local time trends in the original series and is not representative of a recurring autoprojective (arima) ...