For numerical stability, I thought it might be a good idea to scale my data before feeding them into an ARMA GARCH model. I have gone through a few older posts and understand the affect scaling innovations/residuals have on GARCH, but what effect does it have on the ARMA coefficients? Thanks!
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When developing a general purpose time-series software, is it a good idea to make it scale invariant? How would one do that?  I took a time series of around 40 points, and then multiplied by factors ranging from 10E-9 to 10E3 and then ran through the ARIMA functions of Forecast Pro and Minitab. In Forecast Pro, all resulted in the same answer (automatic modeling), whereas in Minitab, they were not. Not sure what Forecast Pro does, but they might just scale up or down all the numbers to a certain scale (let's say 100s) before running the model. Is this good idea in general?
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What is the equation for an ARIMA(1, 1, 0) Model?    Please note that I fit the model to a time series in R and received an "ar1" coefficient of 0.6017 and that was the only coefficient estimate provided by R.
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I'm sorry if this is a broad question but can someone explain to me how to interpret these regression diagnostic plots? I understand the Normal Q-Q show's how normal the spread of the data is, but the other three I am confused by. For the Residuals vs Leverage, what does it mean for a point to be outside of the bounds? What does it mean if the red lines are parabolic and curved like in the first two? Why do we care about residuals, and what do they tell us? I've searched the web multiple times for some guide to interpret these and I can't get any straight forward answers. Any help is appreciated, thank you.
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I am trying to determine the most appropriate degree of difference to start building an arima model for this dataset. I already know that I need a first difference, but there is a seasonal component, and I am not exactly sure where to go from here. I've tried several potential options but I am just not very confident when interpreting these plots. I will include the raw time series plot / acf / pacf plots as well as the first differenced time series / acf / pacf plots. Any help would be fantastic!! Original: Time series:  acf:  pacf:  First Difference:  First diff acf:  First diff pacf:
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Can anyone help me out with this question I found on my practice paper?  The series $\{y_t\}$ is described by $$ y_t = 5+0.3y_{t-1}+\epsilon_t+0.9\epsilon_{t-1}. $$ Identify the specific ARIMA model. What is the mean of the series $\{y_t\}$?  I think it is a ARMA (1,1) process? is that correct? And how do I calculate the mean of the ARMA model? Is it the same as AR model? If it is then $$ E(y_t) = 5/ (1-0.30) = 7.14?$$    The sample ACF and PACF plot of a series are given above. Appraise the patterns and judge which ARIMA model fit the series. Justify your conclusion.  I identified as the AR(4). Is that correct? Since ACF has an exponential decay and PACF has a cut off? Differencing is not needed as the ACF decreases sufficiently to 0.
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I would like to know more details about R issues mentioned in .   For e.g. the first problem still exists in R version 3.0.1  # generate an AR(1) with mean 50 set.seed(66)      # so you can reproduce these results x = arima.sim(list(order=c(1,0,0), ar=.9), n=100) + 50    mean(x)     [1] 50.60668   # the sample mean is close arima(x, order = c(1, 0, 0))     Coefficients:            ar1  intercept  &lt;--  here's the problem         0.8971    50.6304  &lt;--  or here, one of these has to change   s.e.  0.0409     0.8365   *direct copy from the webpage  Theoretical model of above simulation is: $X_t = 5 + 0.9 X_{t-1} + Z_t$, where $\{ Z_t\} $ is the white noise  Is R following particular model convention or is R wrong?  If it is wrong, it is still in R core package and I wonder why it isn't changed.  Also, it would be very helpful if I get some hint on other five issues.
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Background: I have the cross-sectional model:  $Y_{i}  = a + b X_{1,i} + c X_{2,i} + d X_{3,i} + e X_{4,i} + \nu_i$.  The application is corporate finance. So each $Y_i$ is something like the change in return on assets over a 1 year period for firm $i$, and the regressors are typical corporate finance variables.  In corporate finance, very small values of $R^2$ are common, even sometimes $1\%$. My $R^2$ is around $1\%$ but my Adjusted $R^2$ is $-0.2\%$.   I have never seen papers report negative Adjusted $R^2$ but this could just be because they omit the publication of their adjusted $R^2$ when they see that it is negative.   Question  Is there some problem when the adjusted $R^2$ is negative?
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It is a common assumption (and, as far as historical stock market data goes, also proven) that the stock market is always growing if you enlarge the time window long enough . In other words: The stock market always goes up in the long term. Is, therefore, the conclusion valid that you can totally invest as much as you want at any point in time you want and you can never go wrong, if  You diversify strong enough (invest &quot;in the world&quot;) You do not need to urgently sell your assets at any point in time  If yes, all that strategies that rely also on diversified, long-term investments (Dollar-Cost-Averaging &amp; Rebalancing, .. what others do you know?) are just to optimize the yiels, but you'd make profit even without those strategies. Is that correct?
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I'm analyzing a residual plot  of the residuals vs the fitted values.  I'm not quite sure how to interpret this plot since there looks like there is a pattern and the average is not actually zero. There are diagonal straight parallel lines.    I'm working with several ordinal IV's.  Any ideas?
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As I was working my way through my book about statistics, I came across the topic of linear regression. During the chapter the author begins with explaining that you want to minimize the residuals in order to make your y = a + bx as good a fit as possible: I do understand this, but halfway the chapter all of a sudden the residuals change into sum squares of residuals. Why is this done? I have been googling, but couldn't find the right answer. Who would like to help me understand why the sums of squares of the residuals is used instead of just the sums of residuals?  Kind regards, Bas
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I assume it is OK to mix different data transformations in the same analysis. I've had to transform some variables to squared and some to cubed in order to meet normal distribution requirements. I'm assuming that it's OK to then use the transformed variables together for regression analysis?
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this is my first ever question on a website i use frequently!  This time series has given me much trouble over the last couple of days even after extensive googling, I suppose with TS theres no two series that look the same, hence my confusion!   I have the following ACF and PACF plots for my data:    After modelling NUMEROUS models in R (ARMA(p,q), with all combinations of p=0,1,2,3,4 and q=0,1,2,3,4) and looking at their theoretical acf plots, it seems R's auto.arima gave the best model with p=q=2.   But in my work, i don't want to just say i used R and inferred nothing from the ACF plots haha!  I understand that the slightly significant PACF at lag 1 indicates an AR component(?) and that as both plots 'slope off' it suggests a ARMA(p,q) model, but is there anything else im missing????  Also; the ts (in my eyes) seems seasonal, however ironically, no amount of differencing makes a difference, the plot still looks the same no matter what d equals. (R also tells me its not seasonal)  In short:   What does the ACF plots tell me (main) Am i right in not differencing the data   Thanks a bunch!!
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I know that in a regression situation, if you have a set of highly correlated variables this is usually "bad" because of the instability in the estimated coefficients (variance goes toward infinity as determinant goes towards zero).  My question is whether this "badness" persists in a PCA situation.  Do the coefficients/loadings/weights/eigenvectors for any particular PC become unstable/arbitrary/non-unique as the covariance matrix becomes singular?  I am particularly interested in the case where only the first principal component is retained, and all others are dismissed as "noise" or "something else" or "unimportant".  I don't think that it does, because you will just be left with a few principal components which have zero, or close to zero variance.  Easy to see this isn't the case in the simple extreme case with 2 variables - suppose they are perfectly correlated.  Then the first PC will be the exact linear relationship, and the second PC will be perpindicular to the first PC, with all PC values equal to zero for all observations (i.e. zero variance).  Wondering if its more general.
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It's been more than 2 years that I am working on different time series. I have read on many articles that ACF is used to identify order of MA term, and PACF for AR. There is a thumb rule that for MA, the lag where ACF shuts off suddenly is the order of MA and similarly for PACF and AR.   Here is  I followed from PennState Eberly College of Science.   My Question is why is it so? For me even ACF can give AR term. I need explanation of thumb rule mentioned above. I am not able to understand thumb rule intuitively/mathematically that why -  Identification of an AR model is often best done with the PACF. Identification of an MA model is often best done with the ACF rather than the PACF  Please note:- I don't need how but "WHY". :)
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Many investment gurus state that majority of investors fail and then offer a proven "[insert fancy name] investment strategy" that will make you successful. The number usually starts at 90% and often goes up to 99%.   Intuitively, the number makes sense to me. After all this is a zero sum game. Taking into account all different kinds of middle-men the game is actually a negative sum game.   Are there any scientific reports supporting these claims? All I found was a bunch of anecdotes.  Edit: several people noted that losing/failing is a relative term. I agree. What would be interesting is to find research that resulted in a sample of distribution of returns relative to some general market index.
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I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with the auto.arima model in the forecast package in R and a GARCH model on the residuals of the ARIMA model.   Is the procedure of sequentially estimating ARIMA and GARCH model correct or would it have been better to jointly model the mean and the variance of the series? If this were correct, is there a (possibly R) function to do it?
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seems to be a well known and renowned machine learning expert in the field of finance. I am very far from his level, as have not yet finished my PhD in economics, and only have an applied level statistical knowledge. I have encountered a much . I can not say I completely understand all the mathematical parts. But there are some claims in the paper, which seem to completely contradict things, which I have learned on statistics and economics thus far, or at least seem to be illogical for me. For a specific example, the paper under the section Pitfall #4 and Solution #4 suggests, that by differencing time series to make them stationary for classical statistical models (ARIMA etc.) removes the memory of the series and thus makes them lose the predictive power:     The conclusion is that, for decades, most empirical studies have   worked with series where memory has been unnecessarily wiped-out. The   reason this is a dangerous practice is that fitting a memory-less   series will likely lead to a spurious pattern, a false discovery.   Incidentally, this over-differentiation of time series may explain why   the Efficient Markets Hypothesis is still so prevalent among academic   circles: Without memory, series will not be predictive, and   researchers may draw the false conclusion that markets are   unpredictable.   In economics there really is a simplified theoretical model on equity returns, which posits, that it is a memory-less white noise, and the prices (the integrated returns) follow a random walk. But from an empirical perspective, as far as I understand the memory-less attribute of returns pertains only to the individual data points themselves, not the series as a whole. A differentiated series still should have a "collective" memory put together, and it has almost the same information as the integrated version, only lacks a constant value. So it should have the same predictive power as well, should it not? Or it is me, who has a lack of understanding?