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 76.06% per annum.
- WMT price at the close of January 17, 2025 was $91.94 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 29.42% per annum.
- WMT price at the close of January 17, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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: November 17, 2023
End date: January 17, 2025
a = 1.7173
b = 0.0015
s = 0.0307
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 76.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0307) – 1
= 13.05%
November 17, 2023 calculations
Top border of price channel:
Exp(Y965)
= Exp(a + b × X965 + 2 × s)
= Exp(a + b × 1,396 + 2 × s)
= Exp(1.7173 + 0.0015 × 1,396 + 2 × 0.0307)
= Exp(3.9420)
= $51.52
Bottom border of price channel:
Exp(Y965)
= Exp(a + b × X965 – 2 × s)
= Exp(a + b × 1,396 – 2 × s)
= Exp(1.7173 + 0.0015 × 1,396 – 2 × 0.0307)
= Exp(3.8193)
= $45.57
January 17, 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(1.7173 + 0.0015 × 1,823 + 2 × 0.0307)
= Exp(4.6037)
= $99.86
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(1.7173 + 0.0015 × 1,823 – 2 × 0.0307)
= Exp(4.4810)
= $88.33
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 76.06% per annum.
- WMT price at the close of January 17, 2025 was $91.94 and was inside the primary price channel.
Secondary Trend
Start date: December 3, 2024
End date: January 17, 2025
a = 6.2470
b = -0.0010
s = 0.0121
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -29.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0121) – 1
= 4.94%
December 3, 2024 calculations
Top border of price channel:
Exp(Y1,226)
= Exp(a + b × X1,226 + 2 × s)
= Exp(a + b × 1,778 + 2 × s)
= Exp(6.2470 + -0.0010 × 1,778 + 2 × 0.0121)
= Exp(4.5736)
= $96.89
Bottom border of price channel:
Exp(Y1,226)
= Exp(a + b × X1,226 – 2 × s)
= Exp(a + b × 1,778 – 2 × s)
= Exp(6.2470 + -0.0010 × 1,778 – 2 × 0.0121)
= Exp(4.5254)
= $92.33
January 17, 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(6.2470 + -0.0010 × 1,823 + 2 × 0.0121)
= Exp(4.5307)
= $92.82
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.2470 + -0.0010 × 1,823 – 2 × 0.0121)
= Exp(4.4824)
= $88.45
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 29.42% per annum.
- WMT price at the close of January 17, 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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