Pandas
Data Analysis
Resampling

Resampling and Frequency Conversion

Resampling is a fundamental technique in time series analysis that involves changing the frequency of your data observations. Whether you're dealing with irregular data, exploring trends over different time periods, or preparing data for visualization, resampling plays a crucial role in making sense of time-dependent information. In this post, we'll delve into the world of resampling and frequency conversion using the powerful Pandas library.

Introduction to Resampling

Time series data often come in various frequencies and granularities, and resampling is a fundamental technique used to manipulate and transform time series data to different time frequencies or intervals. Resampling is crucial in time series analysis to align data, fill gaps, aggregate data, and perform meaningful analysis.

Why Resampling Matters

Consider a scenario where you have a sales dataset with daily transactions, but you want to analyze sales on a monthly basis to identify trends and patterns. Alternatively, you might have high-frequency sensor data that you want to analyze on an hourly basis. These are just a couple of instances where resampling becomes essential for better analysis and visualization.

The .resample() function

The .resample() function in Pandas is a powerful tool for working with time series data. It allows you to change the frequency of your time series data, performing aggregation or downsampling, as well as upsampling. The primary purpose of resampling is to summarize data over different time intervals, providing a higher-level view of your data's behavior.

Common Frequency Aliases

When resampling time series data, it's convenient to use predefined frequency aliases to easily specify the desired time intervals. Here are some common frequency aliases:

  • 'D' (Daily): Resample data to a daily frequency.
  • 'W' (Weekly): Resample data to a weekly frequency.
  • 'M' (Monthly): Resample data to a monthly frequency.
  • 'A' (Annual): Resample data to an annual frequency.
  • You can also use '6M' or 'Q' for bi-annual or quarterly resampling.

Upsampling (Increasing Frequency)

Upsampling involves increasing the frequency of your time series data, often to analyze it at a more granular level. You might consider upsampling when you have lower-frequency data and need to examine it with higher temporal resolution, or when you need to fill in missing data points between observed data.

Upsampling Techniques

There are several techniques for upsampling, each with its own characteristics:

  • Forward Fill (ffill): This method carries the value of the last observed data point forward in time, effectively repeating the previous value until the next data point occurs.

  • Backward Fill (bfill): Similar to forward fill, this method carries the value of the next observed data point backward in time until the next data point occurs.

  • Interpolation: Interpolation estimates missing values based on the neighboring data points. Common interpolation methods include linear(default), polynomial, and spline interpolation.

Example

Let's create a weekly dummy data and then demonstrate upsampling techniques using forward fill (ffill), backward fill (bfill), and interpolation methods.

import pandas as pd
import numpy as np
 
# Create a weekly dummy data
date_rng = pd.date_range(start='2023-01-01', end='2023-12-31', freq='W')
data = np.random.randint(1, 100, size=(len(date_rng),))
df = pd.DataFrame(data, index=date_rng, columns=['weekly_data'])
 
# Resample to daily frequency
daily_df = df.resample('D').asfreq()
 
# Demonstrate upsampling techniques
# Forward Fill (ffill)
ffill_df = daily_df.ffill()
 
# Backward Fill (bfill)
bfill_df = daily_df.bfill()
 
# Interpolation
interpolation_df = daily_df.interpolate()
 
# Create a new DataFrame combining the results
combined_df = pd.concat([daily_df, ffill_df, bfill_df, interpolation_df], axis=1)
combined_df.columns = ['weekly_data', 'ffill', 'bfill', 'interpolation']
 
# Print the combined DataFrame
print(combined_df.head(10))
            weekly_data  ffill  bfill  interpolation
2023-01-01         26.0     26     26      26.000000
2023-01-02          NaN     26     44      28.571429
2023-01-03          NaN     26     44      31.142857
2023-01-04          NaN     26     44      33.714286
2023-01-05          NaN     26     44      36.285714
2023-01-06          NaN     26     44      38.857143
2023-01-07          NaN     26     44      41.428571
2023-01-08         44.0     44     44      44.000000
2023-01-09          NaN     44     61      46.428571
2023-01-10          NaN     44     61      48.857143

Downsampling (Reducing Frequency)

Downsampling involves reducing the frequency of your time series data, often for summarization and visualization purposes. You might consider downsampling when you have high-frequency data that you want to analyze over longer time intervals or when you want to smooth out noisy data for trend analysis.

Downsampling Techniques

Aggregation functions perform operations on the data points within a specific time interval to generate a single value representing that interval. Common aggregation functions include:

  • Sum: Sums up the values within the interval.
  • Mean: Calculates the average of values within the interval.
  • Median: Finds the middle value within the interval.
  • Min: Identifies the smallest value within the interval.
  • Max: Identifies the largest value within the interval.
  • Count: Counts the number of non-null values within the interval.

Example

Let's use the same "flights" dataset to illustrate downsampling techniques:

# Load the Seaborn's flights dataset
flights_df = sns.load_dataset('flights')
 
# Convert the 'year' and 'month' columns to datetime
flights_df['date'] = pd.to_datetime(flights_df['year'].astype(str) + '-' + flights_df['month'].astype(str))
 
# Set the 'date' column as the index
flights_df.set_index('date', inplace=True)
 
# Downsampling to annual frequency using different aggregation functions
annual_summed = flights_df['passengers'].resample('A').sum()
annual_mean = flights_df['passengers'].resample('A').mean().astype('int')
annual_median = flights_df['passengers'].resample('A').median().astype('int')
annual_min = flights_df['passengers'].resample('A').min()
annual_max = flights_df['passengers'].resample('A').max()
annual_count = flights_df['passengers'].resample('A').count()
 
# Combine the results into a single DataFrame using pd.concat
result_df = pd.concat([annual_summed, annual_mean, annual_median, annual_min, annual_max, annual_count], axis=1)
result_df.columns = ['Sum', 'Mean', 'Median', 'Min', 'Max', 'Count']
 
# Print the combined result DataFrame
print(result_df)
             Sum  Mean  Median  Min  Max  Count
date                                           
1949-12-31  1520   126     125  104  148     12
1950-12-31  1676   139     137  114  170     12
1951-12-31  2042   170     169  145  199     12
1952-12-31  2364   197     192  171  242     12
1953-12-31  2700   225     232  180  272     12
1954-12-31  2867   238     231  188  302     12
1955-12-31  3408   284     272  233  364     12
1956-12-31  3939   328     315  271  413     12
1957-12-31  4421   368     351  301  467     12
1958-12-31  4572   381     360  310  505     12
1959-12-31  5140   428     406  342  559     12
1960-12-31  5714   476     461  390  622     12

In this example, we downsample the passenger data from monthly to annual frequency using .resample('A'). We also applied a range of aggregation functions.

OHLC Resampling

Open-High-Low-Close (OHLC) resampling is commonly used in financial data analysis. It involves summarizing time series data into four values: the opening price, the highest price, the lowest price, and the closing price for a given time interval. The opening price is the price of the asset at the beginning of the interval, the closing price is the price at the end of the interval, and the high and low prices represent the highest and lowest prices during the interval.

Applying OHLC Resampling

Let's understand this with an example:

# Create a DataFrame with high-frequency data
date_rng = pd.date_range(start='2023-01-01', end='2023-01-02', freq='S')  # second frequency
data = np.random.randint(100, 110, size=(len(date_rng),))
df = pd.DataFrame(data, index=date_rng, columns=['Price'])
 
# Resample to OHLC format with a 1-minute frequency
ohlc_df = df.resample('T').ohlc()
 
print(ohlc_df.head())
                    Price                
                     open high  low close
2023-01-01 00:00:00   108  109  100   108
2023-01-01 00:01:00   100  109  100   100
2023-01-01 00:02:00   100  109  100   103
2023-01-01 00:03:00   107  109  100   101
2023-01-01 00:04:00   106  109  100   109

In this example, we create a DataFrame df with per-second frequency data sampled using the S frequency alias. We then use .resample('T') to resample the data to a per-minute frequency and apply .ohlc() to calculate the OHLC values for each minute interval.

The resulting ohlc_df DataFrame will have columns for open, high, low, and close prices for each minute interval. The index of ohlc_df will represent the end time of each minute interval.

OHLC resampling helps in capturing the price movement dynamics over different time intervals, making it easier to analyze trends, volatility, and patterns in financial data.

Cautions and Considerations

Potential Pitfalls in Resampling

Resampling time series data is a valuable technique, but it's essential to be aware of potential pitfalls that can affect the accuracy of your analysis:

  • Aliasing Effects: When resampling data to a lower frequency, you risk losing critical information. High-frequency fluctuations might be masked, leading to inaccurate conclusions. This phenomenon is known as aliasing.

  • Misinterpretation: Aggregation methods used during resampling can sometimes obscure underlying patterns. Over-reliance on aggregated values might overlook nuanced trends.

Importance of Domain Knowledge

While resampling techniques provide structure to time series data, it's crucial to complement these techniques with domain knowledge and understanding of the data's characteristics. Here are some considerations to keep in mind:

  • Business Context: Understand the context in which you're performing the analysis. Are there specific trends or patterns that you're looking for? Does the chosen frequency align with business cycles?

  • Seasonality and Trends: Identify whether your data exhibits seasonality (regular patterns) or trends. Resampling may amplify or dampen these characteristics, impacting your analysis.

  • Data Quality: Resampling can magnify errors and noise. It's important to preprocess and clean your data appropriately before applying resampling techniques.

  • Choosing the Right Frequency: Selecting the right frequency for resampling requires careful consideration. A frequency that's too high might lead to overfitting, while a frequency that's too low might obscure important details.

Case-Specific Approach

Ultimately, the effectiveness of resampling techniques depends on your specific use case. For example:

  • Financial Data: When analyzing financial data, such as stock prices, daily OHLC resampling can provide valuable insights into price movements. However, be cautious of potential biases introduced by the choice of frequency.

  • Sensor Data: In sensor data analysis, choosing the right frequency for resampling depends on the data acquisition frequency and the target analysis goals.

Working with Date and TimeTime-based Indexing