CONV (Convolution Moving Average) is the ultimate tool for the signal processing purist. It doesn't presume to know what kind of smoothing you need; it simply asks for a kernel (a set of weights) and applies it to the data. Want a Gaussian filter? A Sinc filter? A custom edge-detection filter? CONV runs them all.
Convolution is the fundamental operation of digital signal processing (DSP). While traders were busy inventing "new" moving averages by tweaking alpha values, engineers were using convolution to process audio, images, and radar signals for decades. CONV brings this raw power to financial time series, allowing for arbitrary FIR (Finite Impulse Response) filtering.
- $K_0$ multiplies the most recent price (or oldest, depending on convention; the QuanTAlib implementation aligns $K_0$ with the oldest data in the window and $K_{N-1}$ with the newest).
CONV stores the kernel in a pre-allocated array. The `Update` method performs a dot product using a circular buffer for the price history, requiring no new allocations.
Validation is performed by reproducing standard moving averages (SMA, WMA, TRIMA) using their equivalent kernels and comparing against external libraries.
1.**Kernel Direction**: Our implementation applies the kernel such that the last element of the kernel multiplies the most recent data point. If you import kernels from other DSP libraries, you might need to reverse them.
2.**Normalization**: Kernel weights are *not* automatically normalized. If the sum of the weights is not 1.0, the output scale will be different from the input scale. This is a feature, not a bug (allows for differential filters).
3.**Performance**: A kernel size of 1000 will be 100x slower than a kernel size of 10. Use FFT-based convolution for massive kernels (not implemented here; this is for trading, not searching for extraterrestrial life).
