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This is not an R question but if anyone can help me, it's much appreciated. Suppose I have a series ( stationary ) y_t and a series x_t ( stationary )and x_t has variance sigma^2_x and epsilon is normal (0, sigma^2_epsilon ) and the two series have the relation y_t = Beta*x_t + epsilon My question is if there are particular values that sigma^2_x and sigma^2_epsilon have to take in order for corr(x_t,y_t) to equal Beta ? I...

...r the whole 24 weeks and then calculating a statistic from those based on those regressions ? I broke things up into 24 weeks because I was thinking that the stability of the performance difference of the two models could be examined over time. Essentially these are simple time series regressions X_t = B*X_t-1 + epsilon so I always need to consider whether any type of behavior is stable. But now I am thinking that, if I just want one overall number, then maybe I should be considering all the data simultaneously ? In a nutshell, I am looking for any suggestions on the best way to test whet...

For 2 or 3 stage least squares, what do you R folks do? Follow-up question. My student wants to estimate this. 2 variables are governed by a system of difference equations. His theory is like so. Y_t and X_t are state variables, we want estimates for a, g, b, and h. X_(t+1) = 1 + a X_t + (a/K)* (X_t)^2 - g Y_t X_t Y_(t+1) = b Y_t + h* X_t * Y_t K is perhaps something to estimate, but it seems as though somebody has a formula we can use to calculate it from data and people just want to plug in that...

Dear R user, I'm trying to find a solution for optimizing my code. I have to run a 50.000 iteration long simulation and it is absolutely necessary to have an optimized code. I have to do this operation *sum_t ( t(X_t) %*% A %*% X_t )* where X_t is a (d*k) matrix which changes in time and A is a constant in time (d*d) matrix. I have put all my X_t in a three dimensional array X of dimension (d,k,T). At the moment for computing the sum over time I'm doing a for loop and saving the resulting (k*k) matrix in a...

Hi all, I'm new with R (and S), and relatively new to statistics (I'm a computer scientist), so I ask sorry in advance if my question is silly. My problem is this: I have a (sample of a) discrete time stochastic process {X_t} and I want to estimate Pr{ X_t | X_{t-l_1}, X_{t-l_2}, ..., X_{t-l_k} } where l_1, l_2, ..., l_k are some fixed time lags. It will be enough for me to compute #{ X_t=a_t, X_{t-l_1}=a_{t-l_1}, X_{t-l_2}=a_{t-l_2}, ..., X_{t-l_k}=a_{t-l_k} } -------------------------------------------------...

...,d,q), seasonal =list(order=c(P,D,Q), period=s) How can I write an estimated seasonal ARIMA model from the outputs. To be specifically, which sign to use? I know R uses a different signs from S plus. Is it correct that the model is: (1-ar1*B-ar2*B^2-...)(1-sar1*B^s-sar2*B^2s-....)(1-B)^d(1-B^s)^D X_t=(1+ma1*B+ma2*B^2+...)(1+sma1*B^s+sma2*B^2s+....) a_t For example: > m1=arima(koeps,order=c(0,1,1),seasonal=list(order=c(0,1,1),period=4)) > m1 Call: arima(x = koeps, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 1), period = 4)) Coefficients: ma1 sma1 -0.4096 -0.82...

...ry bright people on this list. Suppose I had a time series of data and at each point in time t, I was calculating x bar + plus minus sigma where x bar was based on a moving window of size n and so was sigma. So, if I was at time t , then x bar t plus minus sigma_t would be based on the values of x_t-n+1 through x_t. This is the hard part : Is there a way to back out what the next value(s), x_t+1 would have to be in order to for that value to be either greater than x bar_t+1 plus Z*sigma_t+1 or less than x bar_t+1 plus minus Z*sigma_t+1. where Z is whatever constant ? I started to...

This is a statistics question not an R question. When calculating the sample correlation coefficient cor(x_t,y_t) between say two variables, x_t and y_t t=1,.....n ( one can assume that the variables are in time but I don't think this really matters for the question ), does someone know where I can find any piece of literature that says that each (x_j,y_j) pair has To be independent from the other (x_...

I'd like to estimate time varying coefficients in a linear regression using a Kalman filter. Even if the Kalman Filter seems to be available in some packages I can't figure out how to use it to estimate the coefficients. Is there anyway to do that in R? Any help appreciated Thanks

...is is ok, but what if samples are correlated, nonstationary etc.? Are there limit theorems which for example allow us to claim that for weak dependent, stationary and ergodic time series such a 'marginal distribution w.r. to time' converges to marginal distribution of random variable x_t , defined on basis of joint distribution for (x_1,…,x_T) ? What if the correlation is strong (say stationary and ergodic FARIMA model) ? Many thanks for your input Norton

...where the variance of the disturbances is a function of some exogenous variable. So something like: Y_t = a_0 + a_1 * Y_(t-1) +...+ a_p * Y_(t-p) + b_1 * e_(t-1) +...+ b_q * e_(t-q) + e_t, where e_t ~ N(0, sigma^2_t), and with the variance specified by something like sigma^2_t = exp(beta_t * X_t), where X_t is my exogenous variable. I would be very grateful if somebody could point me in the direction of a library that could fit this (or a similar) model. Thanks, James Kirkby Actuarial Maths and Stats Heriot Watt University

Hello everybody, I've a question about "autoregressive Regressionmodels". Let Y[1],.....,Y[n], be a time series. Given the model: Y[t] = phi[1]*Y[t-1] + phi[2]*Y[t-1] + ... + phi[p]*Y[t-p] + x_t^T*beta + u_t, where x_t=(x[1t],x[2t],....x[mt]) and beta=(beta[1],...,beta[m]) and u_t~(0,1) I want to estimate the coefficients phi and beta. Are in R any functions or packages for "autoregressive Regressionmodel" with special summaries?. I'm not meaning the function "ar&quo...

Hi, sorry for bothering your guys again. I want to simulate 100 AR(1) data with cor(x_t, x_t-1)=rho=0.3. The mean of the first 70 data (x_1 to x_70) is 0 and the mean of the last 30 data (x_71 to x_100) is 2. Can I do it in the following way? x <- arima.sim(list=(ar=0.3), 100) mean <- c(rep(0, 70), rep(2, 30)) xnew <- x+mean If the above code to simulate 100 AR(1) data is...

...he effect of a variable (age) on an outcome (local recurrence: lr). I have built 3 models: - model 1: lr ~ age y = \beta_(a1).age - model 2: lr ~ age + presentation variables (X_p) y = \beta_(a2).age + \BETA_(p2).X_p - model 3: lr ~ age + presentation variables + treatment variables( X_t) y = \beta_(a3).age + \BETA_(p3).X_(p) + \BETA_(t3).X_t Presentation variables include variables such as tumor grade, tumor size, etc... the physician cannot interfer with these variables. Treatment variables include variables such as chemotherapy, radiation, surgical margins (a surrog...

Hello - Here's what I'm trying to do. I want to fit a time series y with ARMA(1,1) + GARCH(1,1), there are also an exogeneous variable x which I wish to include, so the whole equation looks like: y_t - \phi y_{t-1} = \sigma_t \epsilon_t + \theta \sigma_{t-1} \epsilon_{t-1} + c x_t where \epsilon_t are i.i.d. random variables \sigma_t^2 = omega + \alpha \sigma_{t-1}^2 + \beta y_{t-1}^2 I looked through documentation of garchFit() from the fGarch library but didn't find a way to include exogeneous variables like x_t. How do I do that? Thank you very much in adv...

Hi, I need help regarding estimating a linear model where restrictions are imposed on the coefficients. An example is as follows: Y_{t+2}=a1Y_{t+1} + a2 Y_t + b x_t + e_t restriction a1+ a2 =1 Is there a function or a package that can estimate the coefficient of a model like this? I want to estimate the coefficients rather than test them. Thank you for your help Ahmad Abu Hammour -------------- next part -------------- An HTML attachment was scrubbed... URL:...

Hello! Is it possible to use R time series to identificate a process which is subjected to known input? I.e. I have 2 sequences - one is measurements of black box's state and the second is the "force" by which this black box is driven (which is known too) and I want to fit thist two series with AR-process. The "ar" procedure from stats package expects that the force is

Hi I'm computing the correlation between two time-series x_t and y_t-1 (time-series lagged using the lag(y,-1) function) using the cor() function and the returned value is different from the value of ccf() function at the same lag. Any ideas why this is so? Thanks in advance for any hints. Mihnea [[alternative HTML version deleted]]

...ime slots are divided into two categories: Resting time slots (the first 10) Excited time slots (the last 2) I used model: ************pumps_ti = state_t + slugs_i + error_ti slugs and error are normaly distributed pumps_ti - # of pumps for i-th animal and t-th time slot x_t - order of the time slot (x_1 = 1, ..., x_12 = 12) state_t - state_t = 0 for resting time slots (t=1,...,10) state_t = 1 for excited time slots (t=11,12) slugs_i - ith animal, where i = 1,...,25 I would like to find out if the # of pumps depends on the variable state, ass...

...) = alpha*St*Xt Ht the catch for each period t Xt fishing effort for each period t alpha parameter of boat productivity * the dynamic of the fish stock S(t+1) = S(t) + Gt - Ht I would like to modelise the following system: S_(t+1) = S_t + G_t - H_t G_t = r*S_t*(1-S_t / sbar) H_t = alpha * S_t * X_t S_1961 = S_0 I know only H_t on period (1961 - 1994) and X_t on the same period. I don't know r, sbar, alpha and S_0 (the initial level of the stock) (and of course S_t on this period) and I want to estimate this four parameters. I have written something like that: **************************...