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 56.25% per annum.
- VZ price at the close of April 25, 2024 was $39.22 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.92% per annum.
- VZ price at the close of April 25, 2024 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 VZ 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: July 17, 2023
End date: April 19, 2024
a = 1.5154
b = 0.0012
s = 0.0436
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 56.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0436) – 1
= 19.05%
July 17, 2023 calculations
Top border of price channel:
Exp(Y1,062)
= Exp(a + b × X1,062 + 2 × s)
= Exp(a + b × 1,543 + 2 × s)
= Exp(1.5154 + 0.0012 × 1,543 + 2 × 0.0436)
= Exp(3.4890)
= $32.75
Bottom border of price channel:
Exp(Y1,062)
= Exp(a + b × X1,062 – 2 × s)
= Exp(a + b × 1,543 – 2 × s)
= Exp(1.5154 + 0.0012 × 1,543 – 2 × 0.0436)
= Exp(3.3147)
= $27.51
April 19, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(1.5154 + 0.0012 × 1,820 + 2 × 0.0436)
= Exp(3.8277)
= $45.96
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(1.5154 + 0.0012 × 1,820 – 2 × 0.0436)
= Exp(3.6534)
= $38.60
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 56.25% per annum.
- VZ price at the close of April 25, 2024 was $39.22 and was inside the primary price channel.
Secondary Trend
Start date: January 23, 2024
End date: April 25, 2024
a = 3.9385
b = -0.0001
s = 0.0230
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.92%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0230) – 1
= 9.62%
January 23, 2024 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,733 + 2 × s)
= Exp(3.9385 + -0.0001 × 1,733 + 2 × 0.0230)
= Exp(3.7447)
= $42.30
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,733 – 2 × s)
= Exp(3.9385 + -0.0001 × 1,733 – 2 × 0.0230)
= Exp(3.6529)
= $38.59
April 25, 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(3.9385 + -0.0001 × 1,826 + 2 × 0.0230)
= Exp(3.7319)
= $41.76
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.9385 + -0.0001 × 1,826 – 2 × 0.0230)
= Exp(3.6400)
= $38.09
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 4.92% per annum.
- VZ price at the close of April 25, 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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