This is an old revision of the document!
What are the names of theoretical frameworks, in which one might construct models that incorporate assumptions about periodicity and use them to predict future occurrences?
There are several theoretical frameworks and models that incorporate assumptions about periodicity to predict future occurrences. Here are some notable ones:
1. Time Series Analysis: This statistical method analyzes time-ordered data points to identify trends, seasonal patterns, and cyclic behaviors. Techniques like Autoregressive Integrated Moving Average (ARIMA) models and Seasonal Decomposition of Time Series (STL) are commonly used.
Average
2. Fourier Analysis: This mathematical approach decomposes functions or signals into their constituent frequencies. It is often used to identify periodic components in data and can help predict future values based on identified cycles.
Frequencies
3. Harmonic Analysis: Similar to Fourier analysis, harmonic analysis focuses on representing functions as sums of sinusoidal components. It is useful in identifying periodic behavior in various fields, including physics and engineering.
Harmonics
4. Markov Models: These stochastic models can incorporate periodicity by defining states and transition probabilities that may vary with time. Hidden Markov Models (HMMs) can also be used to model sequences with periodic characteristics.
Markov
5. Seasonal Autoregressive Integrated Moving Average (SARIMA): This is an extension of ARIMA that specifically accounts for seasonality in time series data, making it suitable for modeling periodic events.
6. Dynamic Systems Theory: This framework studies systems that evolve over time, often incorporating periodic behavior. It can be used to model and predict the behavior of complex systems with cyclical patterns.
7. Chaos Theory: While primarily focused on deterministic systems that exhibit sensitive dependence on initial conditions, chaos theory can also explore periodic or quasi-periodic behavior in complex systems.
8. Agent-Based Modeling: In this computational approach, individual agents interact according to defined rules, which can include periodic behaviors. This framework can simulate and predict the emergence of patterns over time.
9. Ecological Models: In ecology, models like Lotka-Volterra equations for predator-prey dynamics often incorporate periodicity to predict population cycles.
These frameworks can be applied in various fields, including economics, biology, engineering, and social sciences, to model and predict phenomena that exhibit periodic behavior.