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 31.91% per annum.
- TJX price at the close of September 10, 2024 was $117.83 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 79.49% per annum.
- TJX price at the close of September 10, 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: September 10, 2024
a = 3.3450
b = 0.0008
s = 0.0505
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 31.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0505) – 1
= 22.39%
March 4, 2022 calculations
Top border of price channel:
Exp(Y625)
= Exp(a + b × X625 + 2 × s)
= Exp(a + b × 905 + 2 × s)
= Exp(3.3450 + 0.0008 × 905 + 2 × 0.0505)
= Exp(4.1326)
= $62.34
Bottom border of price channel:
Exp(Y625)
= Exp(a + b × X625 – 2 × s)
= Exp(a + b × 905 – 2 × s)
= Exp(3.3450 + 0.0008 × 905 – 2 × 0.0505)
= Exp(3.9306)
= $50.94
September 10, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.3450 + 0.0008 × 1,826 + 2 × 0.0505)
= Exp(4.8314)
= $125.39
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.3450 + 0.0008 × 1,826 – 2 × 0.0505)
= Exp(4.6294)
= $102.45
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 31.91% per annum.
- TJX price at the close of September 10, 2024 was $117.83 and was inside the primary price channel.
Secondary Trend
Start date: April 4, 2024
End date: September 10, 2024
a = 1.8650
b = 0.0016
s = 0.0275
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 79.49%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0275) – 1
= 11.62%
April 4, 2024 calculations
Top border of price channel:
Exp(Y1,148)
= Exp(a + b × X1,148 + 2 × s)
= Exp(a + b × 1,667 + 2 × s)
= Exp(1.8650 + 0.0016 × 1,667 + 2 × 0.0275)
= Exp(4.5915)
= $98.64
Bottom border of price channel:
Exp(Y1,148)
= Exp(a + b × X1,148 – 2 × s)
= Exp(a + b × 1,667 – 2 × s)
= Exp(1.8650 + 0.0016 × 1,667 – 2 × 0.0275)
= Exp(4.4815)
= $88.37
September 10, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.8650 + 0.0016 × 1,826 + 2 × 0.0275)
= Exp(4.8463)
= $127.27
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.8650 + 0.0016 × 1,826 – 2 × 0.0275)
= Exp(4.7363)
= $114.01
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 79.49% per annum.
- TJX price at the close of September 10, 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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