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 68.18% per annum.
- WMT price at the close of May 23, 2025 was $96.34 and was lower than the bottom border of the primary price channel by $4.38 (4.34%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2.70% per annum.
- WMT price at the close of May 23, 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 WMT 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: September 29, 2023
End date: March 6, 2025
a = 2.1066
b = 0.0014
s = 0.0454
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 68.18%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0454) – 1
= 19.93%
September 29, 2023 calculations
Top border of price channel:
Exp(Y843)
= Exp(a + b × X843 + 2 × s)
= Exp(a + b × 1,221 + 2 × s)
= Exp(2.1066 + 0.0014 × 1,221 + 2 × 0.0454)
= Exp(3.9366)
= $51.24
Bottom border of price channel:
Exp(Y843)
= Exp(a + b × X843 – 2 × s)
= Exp(a + b × 1,221 – 2 × s)
= Exp(2.1066 + 0.0014 × 1,221 – 2 × 0.0454)
= Exp(3.7549)
= $42.73
March 6, 2025 calculations
Top border of price channel:
Exp(Y1,201)
= Exp(a + b × X1,201 + 2 × s)
= Exp(a + b × 1,745 + 2 × s)
= Exp(2.1066 + 0.0014 × 1,745 + 2 × 0.0454)
= Exp(4.6829)
= $108.09
Bottom border of price channel:
Exp(Y1,201)
= Exp(a + b × X1,201 – 2 × s)
= Exp(a + b × 1,745 – 2 × s)
= Exp(2.1066 + 0.0014 × 1,745 – 2 × 0.0454)
= Exp(4.5012)
= $90.13
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 68.18% per annum.
- WMT price at the close of May 23, 2025 was $96.34 and was lower than the bottom border of the primary price channel by $4.38 (4.34%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 21, 2024
End date: May 23, 2025
a = 4.4077
b = 0.0001
s = 0.0535
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.70%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0535) – 1
= 23.86%
November 21, 2024 calculations
Top border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 + 2 × s)
= Exp(a + b × 1,640 + 2 × s)
= Exp(4.4077 + 0.0001 × 1,640 + 2 × 0.0535)
= Exp(4.6345)
= $102.98
Bottom border of price channel:
Exp(Y1,132)
= Exp(a + b × X1,132 – 2 × s)
= Exp(a + b × 1,640 – 2 × s)
= Exp(4.4077 + 0.0001 × 1,640 – 2 × 0.0535)
= Exp(4.4206)
= $83.14
May 23, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.4077 + 0.0001 × 1,823 + 2 × 0.0535)
= Exp(4.6479)
= $104.37
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.4077 + 0.0001 × 1,823 – 2 × 0.0535)
= Exp(4.4339)
= $84.26
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2.70% per annum.
- WMT price at the close of May 23, 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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