Im a beginner in time series analyses.
I need help finding the SARIIMA(p,d,q,P,D,Q,S) parameters.
This is my dataset. Sampletime 1 hour. Season 24 hour.
S=24
Using the adfuller test I get p = 6.202463523469663e-16. Therefor stationary.
d=0 and D=0
Plotting ACF and PACF:
Using this post:
https://arauto.readthedocs.io/en/latest/how_to_choose_terms.html
I learn to "start counting how many “lollipop” are above or below the confidence interval before the next one enter the blue area."
So looking at PACF I can see maybe 5 before one is below the confidence interval. Therefor non seasonal p=5 (AR).
But I having a hard time finding the q - MA parameter from the ACF.
"To estimate the amount of MA terms, this time you will look at ACF plot. The same logic is applied here: how much lollipops are above or below the confidence interval before the next lollipop enters the blue area?"
But in the ACF plot not a single lollipop is inside the blue area.
Any tips?
There are many different rules of thumb and everyone has own views. I would say, in your case you probably do not need the MA component at all. The rule with the lollipop refers to ACF/PACF plots that have a sharp cut-off after a certain lag, for example in your PACF after the second or third lag. Your ACF is trailing off which can be an indicator for not using the MA component. You do not have to necessarily use it and sometimes the data is not suited for an MA model. A good tip is to always check what pmdarima’s auto_arima() function returns for your data:
https://alkaline-ml.com/pmdarima/tips_and_tricks.html
https://alkaline-ml.com/pmdarima/modules/generated/pmdarima.arima.auto_arima.html
Looking at you autocorrelation plot you can clearly see the seasonality. Just because the ADF test tells you it is stationary does not mean it necessarily is. You should at least check if you model works better with seasonal differencing (D).
Related
I have 20 years of data. I want to find the linear trend of the %s as a single number. EG if you were to plot the linear trend, there would be a coefficient by which the line increases/ decreases over time.
Google sheets has a trend function, but it's used for creating new data based on predicting trends.
Your question is too vague to answer clearly and precisely for what you want. Are you looking for the formula for the trend line? Just the correlation coefficient? Or a future value based on the info? The slope of the trend line?
What you have described is linear regression. I would suggest browsing the Insert drop down menu for formulas > statistics. There are formulas for each piece of info you want to draw (except creating the formula for you).
An easy and superficial way of obtaining the correlation coefficient and actual formula (and thus slope for linear trend lines), is to use excel. Copy your data table into excel and then create a scatterplot with the table. Go into the settings for the scatter plot and check the box for “trendline”. Then go into the trendline settings for the plot, and you can select which type of regression you want excel to use. You want linear. Towards the bottom of that menu, you want to check the boxes that say “show formula on chart” and “show R coefficient” or something along those lines. Excel will then print out your formula and coefficient in a text box on the chart. Your slope will be the coefficient of the x variable.
Hope this helps! Regression is a wormhole. I’d love to get more in depth if you’re interested!
NOTE: The outlier for year 2003 will have a significant impact on a linear regression line. Consider removing it from the data to create a line that will be more accurate for future predictions.
I want to quantify seasonal variation to be able to determine that one data has more seasonal variation than another data.
I am analyzing weekday variation in sales for a stores (Store A ). I have data between 1995 and 1999 and 2005 and 2009.
My aim is to identify and compare the daily Seasonality in 1995-1999 and 2004-2009.
I have worked with seasonality before, but I have never used any method to quantify seasonality.
I have identified the seasonal components using the decompose() function in R.
I run two separate models, one for 1995-1999 and one for 2004-2009.
I use additive models because the seasonality does not vary within these periods.
I report the results as seasonal index.
It is easy to see (Figure below) that there was less seasonality in 2005-2009 (dotted line) compared to 1995-1999 (solid).
However, I would like to be able to quantify the difference in seasonality.
Is it correct to use a simple Coefficient of variation (CV)? CV in 1995-1999 = 0.15. CV in 2005-2009 = 0.5.
strength of seasonality
small vs. large seasonality
1]: https://i.stack.imgur.com/ibD44.png
I have read about the strength of seasonality and wonder about what it really indicates. What is the meant of strength of seasonality? feat_stl() function i r produce seasonal_strength. But is this really an indicator of how much seasonality a seasonal pattern holds? Is strength = "how much"
Is not the total area under/above the line of seasonality a better measure of increasing/ declining seasonality. The blue line obviously symbolizes much more seasonal variation compared to the red line. If you measure the arena below/above the lines, these areas also clearly shows this.
Is measuring the total area above/below the line a working way to quantify seasonal variation?
I understand that it can be more complex if the seasonal pattern is very fluctuating because that is also part of seasonal variation.
I have used ARIMA(0,1,0)(0,1,1)12 where seasonal lag is 12. The ACF plot & PACF plot of residuals suggests pattern where as box test for 12 lags, 24 lags etc shows p value in the range of 20% to 40% indicating randomness.
Is it really possible to have contradictory results OR there might be a problem in the way i modeled it.
I am using Arima function of R.
The original series has strong seasonality and upward trend.
Regards
Lakshmi
I'm actually trying to detect characteristics of the time series for a very big region composed of many smaller subregions (in my case pixels). I don't know much about this, so the only way I can come up with is an averaged time series for the entire region, although I know this would definitely conceal many features by averaging.
I'm just wondering if there are any widely used techniques that can detect the common features of a suite of time series? like pattern recognition or time series classification?
Any ideas/suggestions are much appreciated!
Thanks!
Some extra explanations: I'm dealing with remote sensing images of several years with a time step of 7 days. So for each pixel, there is a time series associated, with values extracted from this pixel on different dates.So if I define a region consisting of many pixels, is there a way to detect or extract some common features charactering all or most of the time series of pixels within this region? Such as the shape of the time series, or a date around which there's an obvious increase in the values?
You could compute the correlation matrix for the pixels. This would simply be:
corr = np.zeros((npix,npix))
for i in range(npix):
for j in range(npix):
corr(i,j) = sum(data(i,:)*data(j,:))/sqrt(sum(data(i,:)**2)*sum(data(j,:)**2))
If you want more information, you can compute this as a function of time, i.e. divide your time series into blocks (say minutes) and compute the correlation for each of them. Then you can see how the correlation changes over time.
If the correlation changes a lot, you may be more interested in the cross-power spectrum of the pixels. This is defined as
cpow(i,j,:) = (fft(data(i,:))*conj(fft(data(j,:)))
This will tell you how much pixel i and j tend to change together on various time-scales. For example, they could be moving in unison in time-scales of a second (1 Hz), but also have changes on a time-scale of, say, 10 seconds which are not correlated with each other.
It all depends on what you need, really.
So I've recorded some data from an Android GPS, and I'm trying to find the peaks of these graphs, but I haven't been able to find anything specific, perhaps because I'm not too sure what I'm looking for. I have found some MatLab functions, but I can't find the actual algorithms that do it. I need to do this in Java, but I should be able to translate code from other languages.
As you can see, there are lots of 'mini-peaks', but I just want the main ones.
Your solution depends on what you want to do with the data. If you want to do very serious things then you should most likely use (Fast) Fourier Transforms, and extract both the phase and frequency output from it. But that's very computationally intensive and takes a long while to program. If you just want to do something simple that doesn't require a lot of computational resources, then here's a suggestion:
For that exact problem i implemented the below algorithm a few hours ago. I invented the algorithm myself so i do not know if it has a name already, but it is working great on very noisy data.
You need to determine the average peak-to-peak distance and call that PtP. Do that measurement any what you like. Judging from the graph in your case it appears to be about 35. In my code i have another algorithm i invented to do that automatically.
Then choose a random starting index on the graph. Poll every new datapoint from then on and wait until the graph has either risen or fallen from the starting index level by about 70% of PtP. If it was a fall then that's a tock. If it was a rise then that's a tick. Store that level as the last tick or tock height. Produce a 'tick' or 'tock' event at this index.
Continue forward in the data. After ticks, if the data continues to rise after that point then store that level as the new 'height-of-tick' but do not produce a new tick event. After tocks, if the data continues to fall after that point then store that level as the new 'depth-of-tock' but do not produce a new tock event.
If last event was a tock then wait for a tick, if last event was a tick then wait for a tock.
Each time you detect a tick, then that should be a peak! Good luck.
I think what you want to do is run this through some sort of low-pass filter. Depending on exactly what you want to get out of this dataset, a simple "box car" filter might be
sufficient: at each point, take the average of the N samples centered on that point,
and take the average as the filtered value. The larger N is, the more aggressively smoothed the filtered data will be.
I guess you have lots of points... Calculate mean value of them, subtract it from all point's values and get highest point value (negative or positive) from each range where points have same sign till they change it. I hope I am clear...
With particulary nasty and noisy data I usually use smoothing. Easiest example of smoothing is moving average. Then you can find peacks on that moving average. And then you simply go back to your original data and take the closest peak to one you found on moving average.
I've done some looking into peak detection and I can tell you that if your data doesn't behave, it could mess up your algorithm. Off the top of my head, you could try: Pick a threshold, i.e threshold = 250. If data is above threshold, find the max at that period. This is assuming that the data you have has a mean about 230. Not sure how fancy you want to get. Hope that helps.