# Tag Info

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Unfortunately with the S&P ratings it is unclear when the latest changes were made: http://www.standardandpoors.com/ratings/sovereigns/ratings-list/en/us/?subSectorCode=39&sectorId=1221186707758&subSectorId=1221187348494 If anyone is able to find any historic S&P country credit ratings please post them

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For an Excel and VBA implementation with open source code see here

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You have $$ln\left(x_{t-4}\right)$$ so you don't need to get an estimate for $$ln\left(\widetilde{x}_{t-4}\right)$$ just plug that in, add your forecast for $y_{t}$, then take the exponential.

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You can recover the levels of $X$ at time $t$ if you have $X(0)$ as well as all first differences until $X(t)$. Then $X(t) = X(0) + \sum_{i=1}^t (X(i)-X(i-1))$. In your case $X:=ln(Y)$, apply the above algorithm to find $ln(Y(t))$ from which $Y(t)=e^{X(t)}$.

-1

Simply calculate the cumulative sum. But you still need the intercept/a constant. From differences you cannot get the level of the original series. Tiny example: series: 5,6,7,8 / differences: 1,1,1 / cumulative sum: 1,2,3

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Your question is more about "how to estimate correlations between variables sampled at different frequencies?" than about PCA. After all, PCA is just diagonalization of the covariance (or correlation) matrix, aiming to obtain principal vectors driving the joint dynamics of your variables in an $L^2$ sense. Since data are by construction not synchronized at ...

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You can't include the levels in OLS. You will get biased coefficient and standard error estimates. Look to include this as some sort of ratio with other predictors based on theory, and test the ratio's stationarity. I can't yet imagine how this point would work but think about it. Maybe you can test the order of integration and use multiple differencing. ...

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I would argue that this is the very definition of a non-stationary process. We know that shares outstanding are incrementally added to or removed from by the company issuing or repurchasing shares. These innovations are added to the previous outstanding share count. My first instinct would be to model this as: $$Y_i = Y_{i-1} + dX$$ Or perhaps ...

5

To quote Wikipedia: In mathematics, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time. Consequently, parameters such as the mean and variance, if they are present, also do not change over time and do not follow any ...

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