Downsample time series whenever abs(difference) since the previous sample exceeds threshold

Question

I have a timeseries of intraday tick-by-tick stock prices that change gradually over time. Whenever there is a small change (e.g. the price increases by $0.01), a new row of data is created. This leads to a very large data series which is slow to plot. I want to downsample so that small changes (e.g. the price goes up/down/up/down/up/down and is unchanged after 50 rows of data) are ignored, which improves plotting speed without sacrificing the qualitative accuracy of the graph. I only want to sample if the price goes up/up/up/up so that I am only displaying obvious changes.

import pandas as pd
import numpy as np
prices = pd.DataFrame(np.random.randint(0,1000, size=(100, 1))/100+1000, columns=list('A'))

I wish to sample whenever the difference with the previous sample exceeds some threshold. So, I will sample row 0 by default. If row 1, 2, 3 and 4 are too close to row 0, I want to throw them away. Then, if row 5 is sufficiently far away from row 0, I will sample that. Then, row 5 becomes my new anchor point, and I will repeat the same process described immediately above.

Is there a way to do this, ideally without a loop?

Answer 1

Not exactly what was asked for. I offer two options with a threshold and a threshold and a sliding period.

import pandas as pd
import numpy as np

prices = pd.DataFrame(np.random.randint(0,1000, size=(100, 1))/100+1000, columns=list('A'))

threshold_ = 3
index = np.abs(prices['A'].values[1:] - prices['A'].values[:-1]) > threshold_
index = np.insert(index, 0, True)

print(prices[index == True], len(prices[index == True]))

period = 5
hist = len(prices)
index = np.abs(prices['A'].values[period:] - prices['A'].values[:hist-period]) > threshold_
index = np.insert(index, 0, np.empty((1,period), dtype=bool)[0])

print(prices[index == True], len(prices[index == True]))