time series data : Predict $Y$ with $X$, where $X$ is dependent on $Y$
Let $Y$ be a target variable which you want to predict on using $X$ (e.g with a statistical model), where $X,Yin mathbb{R}$.
You are given data which looks like this :
$$
data_t = (X_t, Y_t), tin {0,1,2,...,n}
$$
You want to predict $Y$ using $X$, but you know that $X$ is not independent, in fact you know that a change in $Y_{t}$ has a causal effect on $X_{t+j}$, where $j$ is not known but $jgeq 1$ $(1)$
$$
X_t = hat{f}(Y_{t-j}, args)
$$
You also know that a change in $X_{t}$ can have a non-causal effect on $Y_{t+j}$ which is not random and not necessary due to a former change in $Y_{t-j}$ $(2)$
$$
Y_t = hat{f}(X_{t-j}, args)
$$
It is very likely that patterns in $X_{ito j}$ can determine $Y_{j}$ or $Y_{j+x}$ $x geq 1$ $(3)$
My Questions :
$(a)$ Given $(1)$ and $(2)$ it is obvious that for example a change in $Y_{t}$ effects $X_{t+1}$ effects $Y_{t+2}$ [...]. Is there a way to extract the effect of $X$ on $Y$ without the bias caused by $Y$ itself?
$(b)$ Which kind of analysis tools should i use to explore this kind of relationship for a large data set? Im Especially interested in finding patterns similar to what i described in $(3)$
$(c)$ How would this scenario change if $X$ would be a set of predictors with $X_{ito n}$, where
i) all predictors $in$ $X$ share the properties described above.
ii) not all predictors share this properties. (In this case why do people drop highly correlated variables?)
Note that question $(c)$ is not as important as $(a)$ and $(b)$ !
I would really appreciate some help here :)
statistics stochastic-processes machine-learning
asked Dec 8 at 16:04
Ekko
12
add a comment |
Let $Y$ be a target variable which you want to predict on using $X$ (e.g with a statistical model), where $X,Yin mathbb{R}$.
You are given data which looks like this :
$$
data_t = (X_t, Y_t), tin {0,1,2,...,n}
$$
You want to predict $Y$ using $X$, but you know that $X$ is not independent, in fact you know that a change in $Y_{t}$ has a causal effect on $X_{t+j}$, where $j$ is not known but $jgeq 1$ $(1)$
$$
X_t = hat{f}(Y_{t-j}, args)
$$
You also know that a change in $X_{t}$ can have a non-causal effect on $Y_{t+j}$ which is not random and not necessary due to a former change in $Y_{t-j}$ $(2)$
$$
Y_t = hat{f}(X_{t-j}, args)
$$
It is very likely that patterns in $X_{ito j}$ can determine $Y_{j}$ or $Y_{j+x}$ $x geq 1$ $(3)$
My Questions :
$(a)$ Given $(1)$ and $(2)$ it is obvious that for example a change in $Y_{t}$ effects $X_{t+1}$ effects $Y_{t+2}$ [...]. Is there a way to extract the effect of $X$ on $Y$ without the bias caused by $Y$ itself?
$(b)$ Which kind of analysis tools should i use to explore this kind of relationship for a large data set? Im Especially interested in finding patterns similar to what i described in $(3)$
$(c)$ How would this scenario change if $X$ would be a set of predictors with $X_{ito n}$, where
i) all predictors $in$ $X$ share the properties described above.
ii) not all predictors share this properties. (In this case why do people drop highly correlated variables?)
Note that question $(c)$ is not as important as $(a)$ and $(b)$ !
I would really appreciate some help here :)
statistics stochastic-processes machine-learning
asked Dec 8 at 16:04
Ekko
12
add a comment |
Let $Y$ be a target variable which you want to predict on using $X$ (e.g with a statistical model), where $X,Yin mathbb{R}$.
You are given data which looks like this :
$$
data_t = (X_t, Y_t), tin {0,1,2,...,n}
$$
You want to predict $Y$ using $X$, but you know that $X$ is not independent, in fact you know that a change in $Y_{t}$ has a causal effect on $X_{t+j}$, where $j$ is not known but $jgeq 1$ $(1)$
$$
X_t = hat{f}(Y_{t-j}, args)
$$
You also know that a change in $X_{t}$ can have a non-causal effect on $Y_{t+j}$ which is not random and not necessary due to a former change in $Y_{t-j}$ $(2)$
$$
Y_t = hat{f}(X_{t-j}, args)
$$
It is very likely that patterns in $X_{ito j}$ can determine $Y_{j}$ or $Y_{j+x}$ $x geq 1$ $(3)$
My Questions :
$(a)$ Given $(1)$ and $(2)$ it is obvious that for example a change in $Y_{t}$ effects $X_{t+1}$ effects $Y_{t+2}$ [...]. Is there a way to extract the effect of $X$ on $Y$ without the bias caused by $Y$ itself?
$(b)$ Which kind of analysis tools should i use to explore this kind of relationship for a large data set? Im Especially interested in finding patterns similar to what i described in $(3)$
$(c)$ How would this scenario change if $X$ would be a set of predictors with $X_{ito n}$, where
i) all predictors $in$ $X$ share the properties described above.
ii) not all predictors share this properties. (In this case why do people drop highly correlated variables?)
Note that question $(c)$ is not as important as $(a)$ and $(b)$ !
I would really appreciate some help here :)
statistics stochastic-processes machine-learning
asked Dec 8 at 16:04
Ekko
12
Let $Y$ be a target variable which you want to predict on using $X$ (e.g with a statistical model), where $X,Yin mathbb{R}$.
You are given data which looks like this :
$$
data_t = (X_t, Y_t), tin {0,1,2,...,n}
$$
You want to predict $Y$ using $X$, but you know that $X$ is not independent, in fact you know that a change in $Y_{t}$ has a causal effect on $X_{t+j}$, where $j$ is not known but $jgeq 1$ $(1)$
$$
X_t = hat{f}(Y_{t-j}, args)
$$
You also know that a change in $X_{t}$ can have a non-causal effect on $Y_{t+j}$ which is not random and not necessary due to a former change in $Y_{t-j}$ $(2)$
$$
Y_t = hat{f}(X_{t-j}, args)
$$
It is very likely that patterns in $X_{ito j}$ can determine $Y_{j}$ or $Y_{j+x}$ $x geq 1$ $(3)$
My Questions :
$(a)$ Given $(1)$ and $(2)$ it is obvious that for example a change in $Y_{t}$ effects $X_{t+1}$ effects $Y_{t+2}$ [...]. Is there a way to extract the effect of $X$ on $Y$ without the bias caused by $Y$ itself?
$(b)$ Which kind of analysis tools should i use to explore this kind of relationship for a large data set? Im Especially interested in finding patterns similar to what i described in $(3)$
$(c)$ How would this scenario change if $X$ would be a set of predictors with $X_{ito n}$, where
i) all predictors $in$ $X$ share the properties described above.
ii) not all predictors share this properties. (In this case why do people drop highly correlated variables?)
Note that question $(c)$ is not as important as $(a)$ and $(b)$ !
I would really appreciate some help here :)
statistics stochastic-processes machine-learning
statistics stochastic-processes machine-learning
asked Dec 8 at 16:04
Ekko
12
asked Dec 8 at 16:04
Ekko
12
asked Dec 8 at 16:04
Ekko
12
asked Dec 8 at 16:04
Ekko
12
asked Dec 8 at 16:04
Ekko
12
12
add a comment |
add a comment |
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