We Keep Coding

Power law test using XY scatter plot

I have Daily Crude oil prices downloaded from FRED, about 10k observations, some values are blank(code cleans them). I believe that I cannot share excel sheets here, so I will just give you a screenshot of what the data looks like:
I calculate the differences and returns and clean up the data but I am kind of stuck.
Here is what the code looks like to get you started:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
data = pd.read_csv("DCOILWTICO.csv")
nan_value = float("NaN")
data.replace("", nan_value, inplace=True)
data.replace(".", nan_value, inplace=True)
data['Previous'] = data['DCOILWTICO'].shift(1)
data.dropna(subset=['Previous'],inplace=True)
data.replace("", nan_value, inplace=True)
data.replace(".", nan_value, inplace=True)
data['DCOILWTICO'] = data['DCOILWTICO'].astype(float)
data['Previous'] = data['Previous'].astype(float)
data['Diff'] = data['DCOILWTICO'] - data['Previous']
data['Return'] = (data['DCOILWTICO'] - data['Previous'])/data['Previous']
Here comes the question: I am trying to duplicate the graph below.(which I believe was generated using Mathematica) The difficult part is to be able to create the bins in the right way. Looking at the graph it looks like there are around 200 bins. On the x-axis are the returns and on the y axis are the frequencies(which have been binned).

I think you are asking how to make equally spaced bins in logspace. If so then use the np.geomspace function (geometric space), rather than np.linspace (linear space).
plt.figure()
bins = np.geomspace(data['returns'].min(), data['returns'].max(), 200)
plt.hist(data['returns'], bins = bins)

compute and plot monthly mean SST anomalies and plot with xarray multindex (pangeo tutorial gallery)

I'm working through the pangeo tutorial gallery and am stuck on the ENSO exercise at the end of xarray
you'll need to download some files:
%%bash
git clone https://github.com/pangeo-data/tutorial-data.git
Then:
import numpy as np
import xarray as xr
import pandas as pd
# load all files
ds_all = xr.open_mfdataset('./tutorial-data/sst/*nc', combine='by_coords')
# slice for enso3.4 region
sst_enso = ds_all.sel(lat=slice(-5,5), lon=slice(-170+360,-120+360))
# subset years to match hint at the bottom
sst_enso = sst_enso.sel(time=sst_enso.time.dt.year>=1982)
# groupby each timepoint and find mean for entire spatial region
avg_enso = sst_enso.sst.groupby('time').mean(dim=['lat','lon'])
avg_enso.plot()
This figure matches that shown at the bottom of the tutorial. so far so good, but i'd like to compute and plot ONI as well. Warm or cold phases of the Oceanic Nino Index are defined by a five consecutive 3-month running mean of sea surface temperature (SST) anomalies in the Niño 3.4 region that is above (below) the threshold of +0.5°C (-0.5°C). This is known as the Oceanic Niño Index (ONI).
I run into trouble because the month becomes an index.
Q1. I'm not sure how to make sure that subtracting sst_enso - enso_clim results in the correct math.
Assuming that is correct, I can compute the regional mean anomaly again and then use a rolling window mean.
enso_clim = sst_enso.sst.groupby('time.month').mean('time')
sst_anom = sst_enso - enso_clim
enso_anom = sst_anom.groupby('time').mean(dim=['lat','lon'])
oni = enso_anom.rolling(time = 3).mean()
Now I'd like to plot a bar chart of oni with positive red, negative blue. Something like this:
for exaample with:
oni.sst.plot.bar(color=(oni.sst < 0).map({True: 'b', False: 'r'}))
Instead oni.sst.plot() gives me:
Resetting the index enso_anom.reset_index('month', drop=True).sst still keeps month as a dimension and gives the same plot. If you drop_dims('month') then the sst data goes away.
I also tried converting to a pd with oni.to_dataframe() but you end up with 5040 rows which is 12 months x 420 month-years I subsetted for. According to the docs "The DataFrame is indexed by the Cartesian product of index coordinates (in the form of a pandas.MultiIndex)." so I guess that makes sense, but not useful. Even if you reset_index of oni before converting to a dataframe you get the same 5040 rows. Q2. Since the dataframe must be repeating itself I can probably figure out where, but is there a way to do this "cleaner" with each date not repeated for all 12 months?

Your code results into an DataArray with the dimensions time and month due to the
re-chunking. This is the reason why you end up with such a plot.
There is a trick (found here) to calculate anomalies. Besides this I would select as a reference period 1986-2015 ( see NOAA definition for ONI-index).
Combining both I ended up in this short code (without the bar plots):
import xarray as xr
import pandas as pd
import matplotlib.pyplot as plt
# load all files
ds_all = xr.open_mfdataset('./tutorial-data/sst/*nc', combine='by_coords')
# slice for enso3.4 region
sst_enso = ds_all.sel(lat=slice(-5,5), lon=slice(-170+360,-120+360))
avg_enso = sst_enso.sst.groupby('time').mean(dim=['lat','lon'])
avg_enso.plot()
ds = sst_enso.sst.mean(dim=['lat','lon'])
enso_clim = ds.sel(time=slice('1986-01-01', '2016-01-01')).groupby("time.month").mean("time")
# ref: https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_change.shtml
enso_anom = ds.groupby("time.month") - enso_clim
# ref: http://xarray.pydata.org/en/stable/examples/weather-data.html#Calculate-monthly-anomalies
enso_anom.plot()
oni = enso_anom.rolling(time = 3).mean()
oni.plot()

How can I remove sharp jumps in data?

I have some skin temperature data (collected at 1Hz) which I intend to analyse.
However, the sensors were not always in contact with the skin. So I have a challenge of removing this non-skin temperature data, whilst preserving the actual skin temperature data. I have about 100 files to analyse, so I need to make this automated.
I'm aware that there is already this similar post, however I've not been able to use that to solve my problem.
My data roughly looks like this:
df =
timeStamp Temp
2018-05-04 10:08:00 28.63
. .
. .
2018-05-04 21:00:00 31.63
The first step I've taken is to simply apply a minimum threshold- this has got rid of the majority of the non-skin data. However, I'm left with the sharp jumps where the sensor was either removed or attached:
To remove these jumps, I was thinking about taking an approach where I use the first order differential of the temp and then use another set of thresholds to get rid of the data I'm not interested in.
e.g.
df_diff = df.diff(60) # period of about 60 makes jumps stick out
filter_index = np.nonzero((df.Temp <-1) | (df.Temp>0.5)) # when diff is less than -1 and greater than 0.5, most likely data jumps.
However, I find myself stuck here. The main problem is that:
1) I don't know how to now use this index list to delete the non-skin data in df. How is best to do this?
The more minor problem is that
2) I think I will still be left with some residual artefacts from the data jumps near the edges (e.g. where a tighter threshold would start to chuck away good data). Is there either a better filtering strategy or a way to then get rid of these artefacts?
*Edit as suggested I've also calculated the second order diff, but to be honest, I think the first order diff would allow for tighter thresholds (see below):
*Edit 2: Link to sample data

Try the code below (I used a tangent function to generate data). I used the second order difference idea from Mad Physicist in the comments.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
df = pd.DataFrame()
df[0] = np.arange(0,10,0.005)
df[1] = np.tan(df[0])
#the following line calculates the absolute value of a second order finite
#difference (derivative)
df[2] = 0.5*(df[1].diff()+df[1].diff(periods=-1)).abs()
df.loc[df[2] < .05][1].plot() #select out regions of a high rate-of-change
df[1].plot() #plot original data
plt.show()
Following is a zoom of the output showing what got filtered. Matplotlib plots a line from beginning to end of the removed data.
Your first question I believe is answered with the .loc selection above.
You second question will take some experimentation with your dataset. The code above only selects out high-derivative data. You'll also need your threshold selection to remove zeroes or the like. You can experiment with where to make the derivative selection. You can also plot a histogram of the derivative to give you a hint as to what to select out.
Also, higher order difference equations are possible to help with smoothing. This should help remove artifacts without having to trim around the cuts.
Edit:
A fourth-order finite difference can be applied using this:
df[2] = (df[1].diff(periods=1)-df[1].diff(periods=-1))*8/12 - \
(df[1].diff(periods=2)-df[1].diff(periods=-2))*1/12
df[2] = df[2].abs()
It's reasonable to think that it may help. The coefficients above can be worked out or derived from the following link for higher orders.
Finite Difference Coefficients Calculator
Note: The above second and fourth order central difference equations are not proper first derivatives. One must divide by the interval length (in this case 0.005) to get the actual derivative.

Here's a suggestion that targets your issues regarding
[...]an approach where I use the first order differential of the temp and then use another set of thresholds to get rid of the data I'm not interested in.
[..]I don't know how to now use this index list to delete the non-skin data in df. How is best to do this?
using stats.zscore() and pandas.merge()
As it is, it will still have a minor issue with your concerns regarding
[...]left with some residual artefacts from the data jumps near the edges[...]
But we'll get to that later.
First, here's a snippet to produce a dataframe that shares some of the challenges with your dataset:
# Imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
np.random.seed(22)
# A function for noisy data with a trend element
def sample():
base = 100
nsample = 50
sigma = 10
# Basic df with trend and sinus seasonality
trend1 = np.linspace(0,1, nsample)
y1 = np.sin(trend1)
dates = pd.date_range(pd.datetime(2016, 1, 1).strftime('%Y-%m-%d'), periods=nsample).tolist()
df = pd.DataFrame({'dates':dates, 'trend1':trend1, 'y1':y1})
df = df.set_index(['dates'])
df.index = pd.to_datetime(df.index)
# Gaussian Noise with amplitude sigma
df['y2'] = sigma * np.random.normal(size=nsample)
df['y3'] = df['y2'] + base + (np.sin(trend1))
df['trend2'] = 1/(np.cos(trend1)/1.05)
df['y4'] = df['y3'] * df['trend2']
df=df['y4'].to_frame()
df.columns = ['Temp']
df['Temp'][20:31] = np.nan
# Insert spikes and missing values
df['Temp'][19] = df['Temp'][39]/4000
df['Temp'][31] = df['Temp'][15]/4000
return(df)
# Dataframe with random data
df_raw = sample()
df_raw.plot()
As you can see, there are two distinct spikes with missing numbers between them. And it's really the missing numbers that are causing the problems here if you prefer to isolate values where the differences are large. The first spike is not a problem since you'll find the difference between a very small number and a number that is more similar to the rest of the data:
But for the second spike, you're going to get the (nonexisting) difference between a very small number and a non-existing number, so that the extreme data-point you'll end up removing is the difference between your outlier and the next observation:
This is not a huge problem for one single observation. You could just fill it right back in there. But for larger data sets that would not be a very viable soution. Anyway, if you can manage without that particular value, the below code should solve your problem. You will also have a similar problem with your very first observation, but I think it would be far more trivial to decide whether or not to keep that one value.
The steps:
# 1. Get some info about the original data:
firstVal = df_raw[:1]
colName = df_raw.columns
# 2. Take the first difference and
df_diff = df_raw.diff()
# 3. Remove missing values
df_clean = df_diff.dropna()
# 4. Select a level for a Z-score to identify and remove outliers
level = 3
df_Z = df_clean[(np.abs(stats.zscore(df_clean)) < level).all(axis=1)]
ix_keep = df_Z.index
# 5. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df_raw.loc[ix_keep]
# 6.
# df_keep will be missing some indexes.
# Do the following if you'd like to keep those indexes
# and, for example, fill missing values with the previous values
df_out = pd.merge(df_keep, df_raw, how='outer', left_index=True, right_index=True)
# 7. Keep only the first column
df_out = df_out.ix[:,0].to_frame()
# 8. Fill missing values
df_complete = df_out.fillna(axis=0, method='ffill')
# 9. Replace first value
df_complete.iloc[0] = firstVal.iloc[0]
# 10. Reset column names
df_complete.columns = colName
# Result
df_complete.plot()
Here's the whole thing for an easy copy-paste:
# Imports
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy import stats
np.random.seed(22)
# A function for noisy data with a trend element
def sample():
base = 100
nsample = 50
sigma = 10
# Basic df with trend and sinus seasonality
trend1 = np.linspace(0,1, nsample)
y1 = np.sin(trend1)
dates = pd.date_range(pd.datetime(2016, 1, 1).strftime('%Y-%m-%d'), periods=nsample).tolist()
df = pd.DataFrame({'dates':dates, 'trend1':trend1, 'y1':y1})
df = df.set_index(['dates'])
df.index = pd.to_datetime(df.index)
# Gaussian Noise with amplitude sigma
df['y2'] = sigma * np.random.normal(size=nsample)
df['y3'] = df['y2'] + base + (np.sin(trend1))
df['trend2'] = 1/(np.cos(trend1)/1.05)
df['y4'] = df['y3'] * df['trend2']
df=df['y4'].to_frame()
df.columns = ['Temp']
df['Temp'][20:31] = np.nan
# Insert spikes and missing values
df['Temp'][19] = df['Temp'][39]/4000
df['Temp'][31] = df['Temp'][15]/4000
return(df)
# A function for removing outliers
def noSpikes(df, level, keepFirst):
# 1. Get some info about the original data:
firstVal = df[:1]
colName = df.columns
# 2. Take the first difference and
df_diff = df.diff()
# 3. Remove missing values
df_clean = df_diff.dropna()
# 4. Select a level for a Z-score to identify and remove outliers
df_Z = df_clean[(np.abs(stats.zscore(df_clean)) < level).all(axis=1)]
ix_keep = df_Z.index
# 5. Subset the raw dataframe with the indexes you'd like to keep
df_keep = df_raw.loc[ix_keep]
# 6.
# df_keep will be missing some indexes.
# Do the following if you'd like to keep those indexes
# and, for example, fill missing values with the previous values
df_out = pd.merge(df_keep, df_raw, how='outer', left_index=True, right_index=True)
# 7. Keep only the first column
df_out = df_out.ix[:,0].to_frame()
# 8. Fill missing values
df_complete = df_out.fillna(axis=0, method='ffill')
# 9. Reset column names
df_complete.columns = colName
# Keep the first value
if keepFirst:
df_complete.iloc[0] = firstVal.iloc[0]
return(df_complete)
# Dataframe with random data
df_raw = sample()
df_raw.plot()
# Remove outliers
df_cleaned = noSpikes(df=df_raw, level = 3, keepFirst = True)
df_cleaned.plot()

Rolling PCA on pandas dataframe

I'm wondering if anyone knows of how to implement a rolling/moving window PCA on a pandas dataframe. I've looked around and found implementations in R and MATLAB but not Python. Any help would be appreciated!
This is not a duplicate - moving window PCA is not the same as PCA on the entire dataframe. Please see pandas.DataFrame.rolling() if you do not understand the difference

Unfortunately, pandas.DataFrame.rolling() seems to flatten the df before rolling, so it cannot be used as one might expect to roll over the rows of the df and pass windows of rows to the PCA.
The following is a work-around for this based on rolling over indices instead of rows. It may not be very elegant but it works:
# Generate some data (1000 time points, 10 features)
data = np.random.random(size=(1000,10))
df = pd.DataFrame(data)
# Set the window size
window = 100
# Initialize an empty df of appropriate size for the output
df_pca = pd.DataFrame( np.zeros((data.shape[0] - window + 1, data.shape[1])) )
# Define PCA fit-transform function
# Note: Instead of attempting to return the result,
# it is written into the previously created output array.
def rolling_pca(window_data):
pca = PCA()
transf = pca.fit_transform(df.iloc[window_data])
df_pca.iloc[int(window_data[0])] = transf[0,:]
return True
# Create a df containing row indices for the workaround
df_idx = pd.DataFrame(np.arange(df.shape[0]))
# Use `rolling` to apply the PCA function
_ = df_idx.rolling(window).apply(rolling_pca)
# The results are now contained here:
print df_pca
A quick check reveals that the values produced by this are identical to control values computed by slicing appropriate windows manually and running PCA on them.

Creating a faceted matplotlib/seaborn plot using indicator variables rather than a single column

Seaborn is great for creating faceted plots based on a categorical variable encoding the class of each facet. However, this assumes your categories are mutually exclusive. Is it possible to create a Seaborn FacetGrid (or similar) based on a set of indicator variables?
As a concrete example, think about comparing patients that are infected with one or more viruses, and plotting an attribute of interest by virus. Its possible that a patient carries more than one virus, so creating a virus column to create a grid on is not possible. You can, however, create a set of indicator variables (one for each virus) that flags the virus for each patient. There does not seem to be a way of passing a set of indicator variables to any of the Seaborn functions to do this.
I can't imagine I'm the first person to come across this scenario, so I'm hoping there are suggestions for how to do this, without coding it by hand in Matploltlib.

I don't see how to do it with FacetGrid, possibly because this isn't facetting the data, since a data-record might appear several times or only once in the plot. One of the standard tricks with a set of bitfields is to read them as binary, so you see each combination of the bits. That's unambiguous but gets messy:
import pandas as pd
import seaborn as sns
from numpy.random import random, randint
from numpy import concatenate
import matplotlib.pyplot as plt
# Dummy data
vdata = pd.DataFrame(concatenate((randint(2, size=(32,4)), random(size=(32,2))), axis=1))
vdata.columns=['Species','v1','v2','v3','x','y']
binary_v = vdata.v1 + vdata.v2*2 + vdata.v3*4
# Making a binary number out of the "virusX?" fields
pd.concat((vdata, binary_v), axis=1)
vdata = pd.concat((vdata, binary_v), axis=1)
vdata.columns=['Species','v1','v2','v3','x','y','binary_v']
# Plotting group membership by row
#g = sns.FacetGrid(vdata, col="Species", row='binary_v')
#g.map(plt.scatter, "x", "y")
#g.add_legend()
#plt.savefig('multiple_facet_binary_row') # Unreadably big.
h = sns.FacetGrid(vdata, col="Species", hue="binary_v")
h.map(plt.scatter, "x","y")
h.add_legend()
plt.savefig('multiple_facet_binary_hue')
If you have too many indicators to deal with the combinatorial explosion, explicitly making the new subsets works:
# Nope, need to pull out subsets:
bdata = vdata[vdata.v1 + vdata.v2 + vdata.v3 ==0.]
assert(len(bdata) > 0) # ... catch...
bdata['Virus'] = pd.Series(['none']*len(bdata), index=bdata.index)
for i in ['v1','v2','v3']:
on = vdata[vdata[i]==1.]
on['Virus'] = pd.Series([i]*len(on), index=on.index)
bdata = bdata.append(on)
j = sns.FacetGrid(bdata, col='Species', row='Virus')
j.map(plt.scatter, 'x', 'y')
j.add_legend()
j.savefig('multiple_facet_refish')