Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 31.93% per annum.
- TJX price at the close of May 20, 2024 was $97.79 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.99% per annum.
- TJX price at the close of May 20, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of TJX price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: March 4, 2022
End date: April 11, 2024
a = 3.2627
b = 0.0008
s = 0.0510
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 31.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0510) – 1
= 22.63%
March 4, 2022 calculations
Top border of price channel:
Exp(Y703)
= Exp(a + b × X703 + 2 × s)
= Exp(a + b × 1,018 + 2 × s)
= Exp(3.2627 + 0.0008 × 1,018 + 2 × 0.0510)
= Exp(4.1376)
= $62.65
Bottom border of price channel:
Exp(Y703)
= Exp(a + b × X703 – 2 × s)
= Exp(a + b × 1,018 – 2 × s)
= Exp(3.2627 + 0.0008 × 1,018 – 2 × 0.0510)
= Exp(3.9336)
= $51.09
April 11, 2024 calculations
Top border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 + 2 × s)
= Exp(a + b × 1,787 + 2 × s)
= Exp(3.2627 + 0.0008 × 1,787 + 2 × 0.0510)
= Exp(4.7214)
= $112.33
Bottom border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 – 2 × s)
= Exp(a + b × 1,787 – 2 × s)
= Exp(3.2627 + 0.0008 × 1,787 – 2 × 0.0510)
= Exp(4.5174)
= $91.60
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 31.93% per annum.
- TJX price at the close of May 20, 2024 was $97.79 and was inside the primary price channel.
Secondary Trend
Start date: November 10, 2022
End date: May 20, 2024
a = 3.6021
b = 0.0005
s = 0.0353
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 21.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0353) – 1
= 15.17%
November 10, 2022 calculations
Top border of price channel:
Exp(Y877)
= Exp(a + b × X877 + 2 × s)
= Exp(a + b × 1,269 + 2 × s)
= Exp(3.6021 + 0.0005 × 1,269 + 2 × 0.0353)
= Exp(4.3636)
= $78.54
Bottom border of price channel:
Exp(Y877)
= Exp(a + b × X877 – 2 × s)
= Exp(a + b × 1,269 – 2 × s)
= Exp(3.6021 + 0.0005 × 1,269 – 2 × 0.0353)
= Exp(4.2224)
= $68.20
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.6021 + 0.0005 × 1,826 + 2 × 0.0353)
= Exp(4.6669)
= $106.37
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.6021 + 0.0005 × 1,826 – 2 × 0.0353)
= Exp(4.5257)
= $92.36
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.99% per annum.
- TJX price at the close of May 20, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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