Questions tagged [filter]

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3
votes
1answer
2k views

What is a density function?

I know about histograms and also know that if we connect the mid-points on the top of bars in a histogram we will get a frequency polygon. This polygon could then be 'smoothed' in a way that it ...
10
votes
2answers
2k views

Wouldn't multiple filters in a convolutional layer learn the same parameter during training?

Based from what I have learned, we use multiple filters in a Conv Layer of a CNN to learn different feature detectors. But since these filters are applied similarly (i.e. slided and multiplied to ...
10
votes
1answer
362 views

Prove/Disprove $E[1_A | \mathscr{F_t}] = 0 ~\text{or} ~ 1 \ \Rightarrow E[1_A | \mathscr{F_{s}}] = E[1_A | \mathscr{F_t}]$

Prove/Disprove $E[1_A | \mathscr{F_t}] = 0 \ \text{or} \ 1 \ \text{a.s.} \ \Rightarrow E[1_A | \mathscr{F_{s}}] = E[1_A | \mathscr{F_t}] \ \text{a.s.}$ Given a filtered probability space $(\Omega, \...
1
vote
1answer
1k views

Filtering using a SARIMA model in R

I am not an expert in statistics, but I would like to work on a SARIMAX model representing power consumption. The exogeneous variable would be the temperature, but for now I found here I might need to ...
2
votes
1answer
609 views

Savitzky-Golay (aka Hodrick–Prescot or Whittaker-Henderson) vs. Kernel

Is there a clear analytic link from Kernel smoothing, particularly the Nadaraya–Watson estimator, (S-G, H-P, or W-H) smoothing filter? The "filter" is called by different names in different fields ...
7
votes
2answers
4k views

Filtering using ARMA model in R

I have two time-series, x and y. I would like to prewhiten x by fitting an ARMA(p,q) (or in ...
4
votes
1answer
2k views

State Space formulation of Hodrick-Prescott filter

I would like to apply the Kalman filter in order to get a causal Hodrick-Prescott filter. The Hodrick-Prescott filter models a time series $(y_t)_{t=0}^T$ as $$ y_t = \tau_t + c_t $$ where $\tau_t$ is ...
5
votes
0answers
687 views

creating random variable with certain auto-correlation in R

I want to create a random variable with a given autocorrelation in R. The target autocorrelation is defined by: $$acf_{target}=(lag+1)^{(-b)}$$ with $b=1.41519$ which I derived from a natural ...
3
votes
2answers
257 views

AIC on Savitzky-Golay width

I want to use a Savitzky-Golay filter to smooth some data. There is a right width to use based on the data that it is smoothing. A number of papers basically use "eyeball norm" on the parameters but ...
1
vote
0answers
106 views

Kalman filter for AR(1) plus noise

I am working the following AR(1) plus noise state-space model $$ z_{t} = x_{t} + v_{t}\\ x_{t} = \phi x_{t-1} + c + w_{t} $$ Therefore, the transition matrix is $[\phi]$, the observation matrix is $[1]...