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Overview

The projection module provides utilities for projecting trends in time series data using linear regression. This is useful for forecasting values based on historical patterns.

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project_trend()

from openavmkit.projection import project_trend

projected_value = project_trend(time_series, time_index)
Fit a linear trend to observed time series values and project the value at a specified time index.

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Parameters

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time_series
np.ndarray
required
Array of observed time series values in chronological order
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time_index
int
required
The array index representing the time period for which you want to predict a value

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Returns

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projected_value
float
The predicted value at the specified time index based on linear trend

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How It Works

The function:
  1. Checks if there are at least 2 data points (required for trend calculation)
  2. If fewer than 2 points, returns the first value (no trend can be calculated)
  3. Fits an Ordinary Least Squares (OLS) linear regression model
  4. Uses the fitted model to predict the value at the requested time index

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Example Usage

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Simple Projection

import numpy as np
from openavmkit.projection import project_trend

# Historical median sale prices by quarter
prices = np.array([250000, 255000, 260000, 265000, 270000])

# Project price for next quarter (index 5)
projected_price = project_trend(prices, time_index=5)
print(f"Projected price: ${projected_price:,.0f}")
# Output: Projected price: $275,000

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Market Trend Analysis

import numpy as np
import pandas as pd
from openavmkit.projection import project_trend

# Quarterly sales data
quarters = pd.date_range('2022-01-01', periods=8, freq='Q')
median_prices = np.array([240000, 245000, 252000, 258000, 
                          265000, 270000, 275000, 278000])

# Project next 4 quarters
projections = []
for i in range(len(median_prices), len(median_prices) + 4):
    proj = project_trend(median_prices, i)
    projections.append(proj)

# Create projection DataFrame
future_quarters = pd.date_range(quarters[-1], periods=5, freq='Q')[1:]
df_proj = pd.DataFrame({
    'quarter': future_quarters,
    'projected_price': projections
})

print(df_proj)

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Insufficient Data Handling

import numpy as np
from openavmkit.projection import project_trend

# Only one data point
single_value = np.array([250000])
projected = project_trend(single_value, 5)

print(f"Projected: ${projected:,.0f}")
# Output: Projected: $250,000 (returns the single value)

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Use Cases

Project market values forward to the assessment’s valuation date when sales data is older than the valuation date.
Analyze and forecast market trends for budget planning and assessment ratio studies.
Normalize historical sales to a common time period for apples-to-apples comparisons.
Estimate missing values in sparse time series data.
This function uses simple linear regression and assumes a constant trend. For more complex patterns, consider using the time adjustment module which supports multiple time trend models.

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Limitations

  • Linear assumption: Assumes a linear trend, which may not hold for volatile or cyclical markets
  • No seasonality: Does not account for seasonal patterns in real estate markets
  • Extrapolation risk: Projections far beyond the observed data may be unreliable
  • Minimum data: Requires at least 2 observations to calculate a trend

Time Adjustment

Advanced time adjustment with multiple models

Ratio Studies

Calculate assessment quality metrics

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