How to fit time series to the curve-linear trend

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Zain 2019-1-24

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评论： Adam Danz 2019-1-25

Hi,

I have fluctuating data with its own curve-linear trend(2) and by polynomial fitting I got curve-linear trend(1). How can I fit fluctuating data(2) to the curve-linear trend(1), so that data are extended by symetric reflection or any kind of data extension?

Like in the figure below.

(Thank you Adam Danz)

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Zain 2019-1-24

编辑：Zain 2019-1-25

在 MATLAB Online 中打开

Line "1" is not covered, it is just polynomial fit trend extension of line "2" trend. I don't want to do any vertical shifting, I want instead of curve (1) to have similar fluctuations as in curve (2). So I tried to multiply 1st 15000* points of data from (2) with the curve (1) and take square root

sqrt(data2(15000:-1:1).*data1)

, but than I get this (around 2 times narrower characteristic than original):

* number of points for which data set is expanded.

Adam Danz 2019-1-24

Ahhh, I see. I'll continue in the answer section below.

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Answer 1

Adam Danz 2019-1-24

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编辑：Adam Danz 2019-1-24

Since your data look approximately normally distributed, you can measure the standard deviation of your data and use that to produce random numbers from a normal distrubution with a mean of your trendline. Here's general instructions.

Step 1: standardize your data by subtracting the mean (which is the trend line): dataStandard = data - trendline

Step 2: calcuate the standard deviation of the standardized data: sd = std(dataStandard)

Step 3: produce random-normal noise with standard deviation calucated in step 2 and the mean will be your red trend line.: newData = normrnd(0, sd, 1, length(trendline)) + trendline.

Step 4: plot the new data: plot(trendline, newData)

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Zain 2019-1-25

Your last solution, I understood as:

dataStandard = data - trendline;

new_data = dataStandard + trendline; new_data = data?

To answer your question - yes, there are no y values between let's say x = 0:15000, that is why I want to symetrically reflect data from x=15001:30001 in a way x(30001:-1:150001) and fit it to follow the trend line.