关于R语言中Croston函数振幅与频率相关参数的技术咨询

Hey there! Let’s break this down clearly first—Croston’s method is built specifically for intermittent time series (think data with lots of zeros, like sporadic product demand). Unlike traditional models (ARIMA, ETS) that directly handle amplitude and frequency, Croston works by splitting your data into two separate components, and its parameters tie indirectly to what you’re asking about.

Key Background #

Croston’s approach splits your time series into:

• Demand size: The non-zero values in your data (this links directly to amplitude, since amplitude refers to the magnitude of variation in your data)
• Demand intervals: The time between consecutive non-zero values (this links to frequency, since frequency is how often non-zero demands occur)

It applies exponential smoothing to both components, then combines them to generate forecasts. Let’s map the parameters to amplitude and frequency using the most common R implementations:

Parameters Tied to Amplitude (Demand Size Variation) #

Amplitude here refers to fluctuations in your non-zero demand values. The parameter controlling how the model reacts to these shifts is:

• alpha_d (in the forecast package’s croston() function) or alpha (default in the tsintermittent package, though you can split it into alpha_d for demand size specifically)
  • This is the smoothing coefficient for the demand size component.
  • A value close to 1 means the model weights recent demand size data heavily—it’ll react quickly to sudden changes in amplitude (like big spikes or drops in non-zero values).
  • A value close to 0 means the model smooths out short-term fluctuations, prioritizing the long-term average of demand size (so it’ll be less responsive to amplitude shifts).

Parameters Tied to Frequency (Demand Occurrence Rate) #

Frequency here refers to how often non-zero demands happen (shorter intervals = higher frequency). The parameter controlling this is:

• alpha_p (available in both forecast and tsintermittent packages)
  • This is the smoothing coefficient for the demand interval component.
  • A value close to 1 means the model prioritizes recent interval data—it’ll adapt quickly to changes in demand frequency (e.g., if demands start happening more often, the model will update fast).
  • A value close to 0 means the model relies on long-term average intervals, ignoring short-term shifts in how often demands occur.

Quick Example in R #

Let’s use the forecast package to see this in action:

# Load the required package
library(forecast)

# Simulate an intermittent time series (mix of zeros and non-zero demands)
intermittent_data <- ts(c(0, 0, 6, 0, 4, 0, 0, 8, 0, 3), frequency = 1)

# Fit Croston's model with custom amplitude/frequency-related parameters
croston_fit <- croston(intermittent_data, alpha_d = 0.3, alpha_p = 0.2)

# Generate 5-step forecasts
croston_forecast <- forecast(croston_fit, h = 5)
print(croston_forecast)

In this code:

• alpha_d = 0.3 makes the model moderately responsive to changes in demand size (amplitude)
• alpha_p = 0.2 makes it slightly slower to adapt to changes in demand frequency

A Quick Note #

Croston’s method doesn’t have "direct" frequency parameters like you’d find in Fourier-transform based models or seasonal ARIMA. If your intermittent data has a clear seasonal pattern, you might want to combine Croston with seasonal adjustments, but the core parameters tied to amplitude/frequency are the smoothing coefficients above.

内容的提问来源于stack exchange，提问作者carlynn