Nadaraya-Watson Envelope (NWE)

Warmup Window

Minimum bars needed: lookback bars (default params: 500 bars (lookback=500))

The Gaussian kernel regression uses a rolling window of lookback bars. Before that many bars are available, the regression is computed over fewer points. After warmup, the indicator updates in real-time.

✅ After the warmup window is filled, this indicator produces a new value on every incoming bar in real-time.

Lagging Indicator

The kernel regression line and bands lag behind price. Bandwidth controls the tradeoff.

Event	Lag	Detail
NWE line reacts to price reversal	bandwidth-dependent	Higher bandwidth = more smoothing = more lag; no fixed bar count
Bands widen/narrow after volatility change	bandwidth-dependent	Bands derived from ATR-scaled offsets of the regression line

Formula for custom params: lag depends on bandwidth (default 8.0); higher = smoother = more lag

The Nadaraya-Watson Envelope uses Gaussian kernel regression to create a smoothed price estimate, then adds an envelope based on the mean absolute error (MAE) scaled by a multiplier. This is a non-repainting (endpoint) implementation. It is useful for identifying overbought/oversold zones and mean-reversion opportunities.

Calculation:

• Kernel weights: w(i) = exp(-i² / (2 × h²)) for i = 0..lookback-1
• Smoothed value: sum(src[t-i] × w(i)) / sum(w(i))
• MAE: SMA of |src - smoothed| over the lookback period
• Upper: smoothed + mult × MAE
• Lower: smoothed - mult × MAE

def nadaraya_watson_envelope(
    data: Union[PdDataFrame, PlDataFrame],
    source_column: str = 'Close',
    bandwidth: float = 8.0,
    mult: float = 3.0,
    lookback: int = 500,
    upper_column: str = 'nwe_upper',
    lower_column: str = 'nwe_lower',
    middle_column: str = 'nwe_middle',
) -> Union[PdDataFrame, PlDataFrame]:

Example

from investing_algorithm_framework import download

from pyindicators import nadaraya_watson_envelope

pl_df = download(
    symbol="btc/eur",
    market="binance",
    time_frame="1d",
    start_date="2023-12-01",
    end_date="2023-12-25",
    save=True,
    storage_path="./data"
)
pd_df = download(
    symbol="btc/eur",
    market="binance",
    time_frame="1d",
    start_date="2023-12-01",
    end_date="2023-12-25",
    pandas=True,
    save=True,
    storage_path="./data"
)

# Calculate Nadaraya-Watson Envelope for Polars DataFrame
pl_df = nadaraya_watson_envelope(pl_df, source_column="Close", bandwidth=8.0, mult=3.0)
pl_df.show(10)

# Calculate Nadaraya-Watson Envelope for Pandas DataFrame
pd_df = nadaraya_watson_envelope(pd_df, source_column="Close", bandwidth=8.0, mult=3.0)
pd_df.tail(10)

Support and Resistance

Indicators that help identify potential support and resistance levels in the market.

Chart Parameters

The image above uses the following parameters:

Parameter	Value
source_column	Close
bandwidth	8.0
mult	3.0
lookback	500