Can you forecast an independent white noise series? At any time white nose is uncorrelated with...
Can you forecast an independent white noise series? At any time white nose is uncorrelated with anything in the past. What happens if the future is uncorrelated with anything in the present or past?
Homework Answers
If it is an independent white noise, it can not be predicted.
Since it is independent in nature, it can not be predicted based on dependent variables.
Now, since it is a white noise, the future has no correlation with the past, thus there is no meaning of using past data to predict the future.
Thus, by definition, an independent white noise can not be predicted.
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Can you forecast an independent white noise series? At any time
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(White noise is not necessarily i.i.d.). Suppose that {Wt} and {Zt} are independent and identically distributed...
(White noise is not necessarily i.i.d.). Suppose that {Wt} and
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P(Wt = 0) = P(Wt = 1) = 1/2 and P(Zt = −1) = P(Zt = 1) = 1/2.
Define the time series Xt by Xt =
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w (1 – W-1) ZŁ
Time Series
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4. Calculate the variance of the time series rt (i.e. Var(rt)) for the following ARMA(1,1) model: where the variance of the white noise series is 0.09.
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: Assume Yt is a time series process and Et is a white noise process with...
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2. A diode can be used as a white noise generator. Calculate the magnitude of shot noise if 100 V is applied to a diode in series with a 10 Ω resistor when measured with an instrument that has a 1...
2. A diode can be used as a white noise generator. Calculate the magnitude of shot noise if 100 V is applied to a diode in series with a 10 Ω resistor when measured with an instrument that has a 100 kHz bandwidth. a. If the shot noise signal above is taken across the resistor and amplified by 105 calculate the shot noise at the amplifier output b.
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3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s...
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(White noise is not necessarily i.i.d.). Suppose that {Wt} and
{Zt} are independent and identically distributed (i.i.d.)
sequences, also independent of each other, with
P(Wt = 0) = P(Wt = 1) = 1/2 and P(Zt = −1) = P(Zt = 1) = 1/2.
Define the time series Xt by Xt =
. Show that {Xt} is white but not i.i.d.
w (1 – W-1) ZŁ
4. Calculate the variance of the time series rt (i.e. Var(rt)) for the following ARMA(1,1) model: where the variance of the white noise series is 0.09.
4. Calculate the variance of the time series rt (i.e. Var(rt)) for the following ARMA(1,1) model: where the variance of the white noise series is 0.09.
2. A diode can be used as a white noise generator. Calculate the magnitude of shot noise if 100 V is applied to a diode in series with a 10 Ω resistor when measured with an instrument that has a 100 kHz bandwidth. a. If the shot noise signal above is taken across the resistor and amplified by 105 calculate the shot noise at the amplifier output b.
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