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 31.90% per annum.
- TJX price at the close of February 20, 2025 was $122.98 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.76% per annum.
- TJX price at the close of February 20, 2025 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 7, 2022
End date: February 20, 2025
a = 3.4627
b = 0.0008
s = 0.0477
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 31.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0477) – 1
= 21.02%
March 7, 2022 calculations
Top border of price channel:
Exp(Y514)
= Exp(a + b × X514 + 2 × s)
= Exp(a + b × 745 + 2 × s)
= Exp(3.4627 + 0.0008 × 745 + 2 × 0.0477)
= Exp(4.1232)
= $61.76
Bottom border of price channel:
Exp(Y514)
= Exp(a + b × X514 – 2 × s)
= Exp(a + b × 745 – 2 × s)
= Exp(3.4627 + 0.0008 × 745 – 2 × 0.0477)
= Exp(3.9324)
= $51.03
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.4627 + 0.0008 × 1,826 + 2 × 0.0477)
= Exp(4.9432)
= $140.22
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.4627 + 0.0008 × 1,826 – 2 × 0.0477)
= Exp(4.7524)
= $115.87
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 31.90% per annum.
- TJX price at the close of February 20, 2025 was $122.98 and was inside the primary price channel.
Secondary Trend
Start date: October 26, 2022
End date: February 20, 2025
a = 3.5634
b = 0.0007
s = 0.0402
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0402) – 1
= 17.45%
October 26, 2022 calculations
Top border of price channel:
Exp(Y676)
= Exp(a + b × X676 + 2 × s)
= Exp(a + b × 978 + 2 × s)
= Exp(3.5634 + 0.0007 × 978 + 2 × 0.0402)
= Exp(4.3212)
= $75.28
Bottom border of price channel:
Exp(Y676)
= Exp(a + b × X676 – 2 × s)
= Exp(a + b × 978 – 2 × s)
= Exp(3.5634 + 0.0007 × 978 – 2 × 0.0402)
= Exp(4.1603)
= $64.09
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.5634 + 0.0007 × 1,826 + 2 × 0.0402)
= Exp(4.9084)
= $135.43
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.5634 + 0.0007 × 1,826 – 2 × 0.0402)
= Exp(4.7476)
= $115.31
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.76% per annum.
- TJX price at the close of February 20, 2025 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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