Questions tagged [time-series]

This tag is used for question related to time series models such as AR, ARMA, ARCH, GARCH and their properties and techniques used for inference.

A time-series model is one which postulates a relationship amongst a num- ber of temporal sequences or time series. An example is provided by the simple regression model

$$y(t) = x(t) \beta + \epsilon(t)$$

or more commonly,

$$y(t) = \sum_{i=1}^p \phi_i y(t-i)+ \sum_{i=1}^k \beta_i y(t-i)+\sum_{i=1}^q \mu_i \epsilon(t-i)$$

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Time Series: Exponential smoothing with seasonality - Why must the average value of multiplicative seasonality factors be 1?

I'm an undergraduate student of applied mathematics and while I was studying time series models I encountered this proposition in my text book that I don't understand. The particular time model is this one: $F_{t,h}= \hat B_t\cdot\hat S_{t+h-s} $…
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Is forecasting appropriate for a seemingly random time-series?

Here's the problem : Each day, a number of virtual machines are created by users. I would like to forecast one day ahead how many virtual machines will be created during the next day. I have at my disposal a time-series representing the number of…
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Estimating ARMA coefficients

Is recursive least square to estimate coefficients of ARMA(p,q) is equivalent to newton's method of finding coefficients using this - $$C_{m+1}=C_m+(X^TV_mX)^{-1}X^T(Y-P_m)$$ EDIT: I've used that equation in logistic regression to find…
user429311
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How to prove the invertibility of a MA series?

In moving-average time series, I was told that the condition for a MA series $Y_t=\Theta(B)Z_t$ to be invertible is for all the roots of $\Theta(B)=0$ lying outside the unit circle. However I only found the proof for MA(1). I wonder what is the…
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Auto-covariance function

For the auto covariance function I'm not to understand how the simplification from the second equals to sign to the third has been done. Any help would be much appreciated.
user134785
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independent and identically distributed Time series

Take a time series $S_t = \left\{ {S_1 ,S_2 ,S_3 ,...,S_n } \right\}$, where $S_t$ are a sequence of numerical data points in successive order, occurring in uniform intervals of time "t". In this case, how can I verify analytically if $ \left\{…
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time series smoothing techniques

I am currently analyzing time series data relating to financial observations (revenue and number of deposits in particular). I would like to smoothen the data because a lot of outliers are present. Which is the most suitable smoothing filter in this…
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Signal and Noise with every day examples

Yesterday a friend asked me what is a signal and noise. When I described him he wasn't satisfied and he told me to give him an everyday example. What kind of example would you use to describe them as simple as possible?
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creating time series

I want to generate a time series length 400. I used the following code beta1=0 e=rnorm(1) out=matrix(NA,400,1) for (i in 1:400){ beta1[i+1]=((exp(0.3*beta1[i]+e)-1)/(1+exp(0.3*beta1[i]+e))) out[i]=beta1[i] } beta1=out beta1=ts(beta1) but the series…
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Single opperation to change the frequency of data

I am looking for a mathematical operation that can help me express daily data as weekly and monthly. I mean that I have $100$ daily observations and I am trying to produce an equation of the form $$ V=C+x_{1}V_{d}+x_{2}V_{w}+x_{3}V_{m}, $$ where $C$…
Docksan
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