New answers tagged time-series
$W_t$ and $B_t$ are tow independent Brownian motion, where : $W_t$ ~ $N(0, s^2_1)$, $B_t$ ~ $N(0, s^2_2)$ $Cov(W_t,B_t)=0$ We know that sum of two Gaussian random variable is also Gaussian. $$E(1/2(W_t+B_t)) = 1/2(E(W_t+B_t))=0$$ $$Var(1/2(W_t+B_t))=1/4(var(W_t+B_t))=1/4(s^2_1+s^2_2)$$ because $W_t and B_t$ are independent. So: $1/2(B_t+W_t)$ ~ $N(0, ...
"Trading a ratio" is called statistical arbitrage or pairs trading. The key here is "cointegration" between two series, i.e. even if 2 series may be non-stationary, their linear combination is. To check statistically if 2 series are cointegrated you may try Dickey-Fuller test. That was theory. Practically speaking, from the plot you presented 2 series do ...
Let me try to explain it. What I will do is to check if the ratio is increasing or decreasing. I mean, if the difference between the two assets is getting bigger or smaller. In this case, the difference among corn and soybeans. What I did is just consider it as an independant portfolio with only two assets, and buying or selling depending on the slope of ...
Intuitively: empirical research has shown that options on the S&P are priced at a slightly higher implied vol than the actual historical vol of the S&P (on average). Why? Likely this is because holding these options provides insurance against bad states of the economy (volatility increases when the economy is in trouble); this is valuable and raises ...
This book by Shumway and Stoffer (two Pitt Stats profs) is excellent IMO: Time Series Analysis and Its Applications: With R Examples (Springer Texts in Statistics): 9781441978646 http://www.amazon.com/Time-Series-Analysis-Its-Applications/dp/144197864X
There is no magic in the Kalman Filter. The linear regression model usually assumes the coefficients follow a random walk and as such it essentially boils down to an estimation followed by exponential smoothing of the coefficients.
Yes, linear regression can be cast as a Kalman filter estimate. I believe, D. Simons book "Optimal State Estimation: .. " has all the details.
There is no a "yes/no answer" to that question. Generally Kalman Filter tends to be better than linear regression, but everything depends on the data which you have, how you calibrate your model. I expect that you have used some library for estimating linear regression parameters. Now you need to think how will you "tune" Kalman filter - the constants ...
Disclosure: I work for the company developing ATSD. Axibase Time-Series Database is not open-source but its community edition is free. Time precision is milliseconds. Value is float, double or long. It supports OLCH period aggregators (first, min, last, max) as well as min_value_time and max_value_time aggregators: min_value_time Time when the minimum ...
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