title: Ð¡ÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð° Ð¿Ð¾Ð³Ð¾Ð´Ñ*
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Statistical methods of weather forecasting
Creators: name: ÐÐ°ÐºÐ¾Ð²ÐµÐµÐ², ÐÐµÐ²
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·
Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ ÑÑÐ´
Ð¿ÑÐ¾Ð³Ð½Ð¾Ð· Ð¿Ð¾Ð³Ð¾Ð´Ñ
ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ
Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ
forecast
time series
weather forecast
statistical model
machine learning

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÑ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ð´Ð»Ñ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾Ð³Ð¾Ð´Ñ Ð² Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³Ðµ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ»Ð° Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð° Ð·Ð°Ð´Ð°ÑÐ° Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð° Ð¿Ð¾Ð³Ð¾Ð´Ñ Ð¸ Ð´Ð°Ð½Ð¾ Ð¿Ð¾Ð½ÑÑÐ¸Ðµ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÑÐ´Ð° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÑÐ´Ð°. ÐÐ±Ð¾Ð·ÑÐµÐ½Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÐ¾Ðµ Ð¸Ð·Ð²ÐµÑÑÐ½ÑÐµ Ð¼ÐµÑÑÐ¸ÐºÐ¸ Ð´Ð»Ñ ÑÐ¾ÑÐ¼Ð°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð². ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¸Ð·Ð²ÐµÑÑÐ½ÑÑ Ð¼ÐµÑÑÐ¸Ðº Ð±ÑÐ»Ð° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð° Ð¸ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð° ÑÐ»ÑÑÑÐµÐ½Ð½Ð°Ñ Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð°Ñ Ð¼ÐµÑÑÐ¸ÐºÐ°, ÑÐ¿ÐµÑÐ¸Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð°Ñ Ð´Ð»Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð° Ð¿Ð¾Ð³Ð¾Ð´Ñ Ð² Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³Ðµ. Ð¡ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð²ÑÐ²ÐµÐ´ÐµÐ½Ð½Ð¾Ð¹ Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð¾Ð¹ Ð¼ÐµÑÑÐ¸ÐºÐ¸ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ»Ð¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ñ, Ð¸ÑÐ¿ÑÑÐ°Ð½Ñ Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ð¾Ñ ÑÐ°Ð¼ÑÑ Ð¿ÑÐ¾ÑÑÑÑ Ð´Ð¾ ÑÐ°Ð¼ÑÑ ÑÐ»Ð¾Ð¶Ð½ÑÑ, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾ Ð½Ð°Ð¸Ð²Ð½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð°Ð²ÑÐ¾ÑÐµÐ³ÑÐµÑÑÐ¸Ð¾Ð½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ, Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐºÐ¾Ð»ÑÐ·ÑÑÐµÐ³Ð¾ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾ Ð¸ ARMA-Ð¼Ð¾Ð´ÐµÐ»Ñ, ÑÐ¾Ð²Ð¾ÐºÑÐ¿Ð»ÑÑÑÐ°Ñ Ð´Ð²Ðµ Ð¿ÑÐµÐ´ÑÐ´ÑÑÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð° Ð²ÑÐ²ÐµÐ´ÐµÐ½Ð° Ð»ÑÑÑÐ°Ñ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð´Ð»Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð° Ð¿Ð¾Ð³Ð¾Ð´Ñ Ð² Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³Ðµ â ARMA(8,8). ÐÐ¼ÐµÑÑÐµ Ñ ÑÐ¸ÑÑÐ¾ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼Ð¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ» ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½ Ð¼ÐµÑÐ¾Ð´ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾ Ð¼ÐµÑÐ¾Ð´ ÑÐ»ÑÑÐ°Ð¹Ð½Ð¾Ð³Ð¾ Ð»ÐµÑÐ°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾, ÑÑÐ¾ Ð¼Ð¾Ð´ÐµÐ»Ñ ARMA(8,8) Ð¸ Ð¼ÐµÑÐ¾Ð´ ÑÐ»ÑÑÐ°Ð¹Ð½Ð¾Ð³Ð¾ Ð»ÐµÑÐ° Ð¿ÑÐ¸Ð¼ÐµÑÐ½Ð¾ Ð¾Ð´Ð¸Ð½Ð°ÐºÐ¾Ð²Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÑÑ Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð½Ð° Ð½ÐµÐ±Ð¾Ð»ÑÑÐ¸Ðµ ÑÐ°ÑÑÑÐ¾ÑÐ½Ð¸Ñ (1 Ð´ÐµÐ½Ñ), Ð½Ð¾ Ð´Ð»Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð° Ð±Ð¾Ð»ÐµÐµ Ð´Ð°Ð»ÑÐºÐ¸Ðµ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÐµ ÑÑÐ°ÑÑÐºÐ¸ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¼ÐµÑÐ¾Ð´ â Ð¾Ð½ ÑÐ¿ÑÐ°Ð²Ð»ÑÐµÑÑÑ Ð½ÐµÐ¼Ð½Ð¾Ð³Ð¾ Ð»ÑÑÑÐµ.
description: This work is devoted to the study and construction of basic statistical time series models for further solving the problem of weather forecasting in St. Petersburg. The work posed the problem of weather forecasting and gave the concept of forecasting a time series using a mathematical model of a time series. Some well-known metrics for formalizing results and comparing time series models are reviewed. Based on known metrics, an improved weighted metric was constructed and justified, specialized for the task of weather forecasting in St. Petersburg. Using the derived weighted metric, the work built, tested and compared various time series models from the simplest to the most complex, namely naive models, an autoregressive model, a moving average model and an ARMA model combining the two previous models. As a result, the best statistical model for weather forecasting in St. Petersburg was derived - ARMA(8,8). Together with purely statistical methods for forecasting time series, the work considered a machine learning method, namely the random forest method. As a result, it was found that the ARMA(8,8) model and the random forest method cope approximately equally well with forecasting over short distances (1 day), but for forecasting over longer time periods it is necessary to use a statistical method - it copes a little better.